Grey Knights - Strengths
We'll start with the Grey Knights because a lot of these strengths play into Tyranid weaknesses or disabuse what we would normally call Tyranid strengths. We'll start with the most obvious - Fortitude. Tyranid firepower is based around suppression and most lists at 1750+ will have around five units which will reliable but out five different damage results a turn. They can have issues killing tanks but when you're stopping half a mech army from moving/shooting, that's pretty good. Grey Knights laugh at this thanks to Fortitude and with only short-ranged psychic defenses, Fortitude can be a real pain on backfield tanks for Tyranids to deal with. If they cannot suppress tanks, the enemy firepower is not reduced and they maintain their mobility. This makes it hard for Tyranids to crack tanks in combat and that their expensive units which reliably cause suppression become highly inefficient. Add in Shrouding for potential 3+ cover as well and Tyranids find Grey Knight tanks a royal pain.
To further this advantage for Grey Knights - their tanks mean less. Certainly Psyfledreads are the shiz and really hurt Tyranids in being able to instant death T4/W3 creatures (but stats tell us less than two will die a turn per Psyfledread) but for the most part, Grey Knights fight outside their vehicles. This nearly doubles the targets Tyranids have to deal with and again, their ranged anti-infantry isn't that flash. Hive Guard, Zoans, T-Fexes, etc. will all find themselves unable to suppress tanks and can little benefit when they do kill them as no infantry is exposed. Sometimes this will be the case (Rhinos with Psycanons inside, Henchmen, Psyfeldreads, etc.) but it's a double whammy in terms of anti-tank and number of targets for Tyranids.
We then get the firepower - everything in the Grey Knights army is generally going to have an excellent target at which to shoot. A lot of S5-8 firepower with good rates of fire will be able to put lots of wounds on T6 targets whilst the mass of S4/5 storm bolters can quickly make a gooey mist of the gribblies. Henchmen based armies may have less of this firepower if they are hiding in their transports but will then often have more high strength firepower with low AP which to throw at the big Tyranids. Add in all this firepower is mobile and the Tyranids have to advance under fire which is moving away from them. Like Imperial Guard, Grey Knights can put a lot of wounds on the tough Tyranid targets and care little about cover. They drop you by forcing wounds.
Let's chuck in some Nemesis Force Weapons for good measure shall we? This is one of the "omg GK breaks Tyranids cheese" cries of many people on the Internet but the fact is, it's not that big. What is big, is having that tiny chance of being able to instant death a full wound T6/W6 Tyranid. It's not going to happen often but unlike against other armies, throwing MCs into combat to attrition units down or simply dominate combat, does not work against Grey Knights. Add in they are ignoring armor saves regardless and even without instant death, your basic squad of Grey Knights has pretty good utility against MCs in combat.
We then get Sanctuary - the power that nearly every Grey Knight should aim to get as this power simply screws up a lot of combat based armies and Tyranids are one of them. With no offensive grenades, Tyranids will be striking last against Sanctuary armies and losing models on the way in. They get Venomthropes the bastards! Not only does this mean Grey Knights can fight in the open (particularly since there are no low AP Tyranid guns) but this combines great with some other options Grey Knights have such as Halberds and Cleansing Flame. Cleansing Flame is the icing on the cake which can wreck horde based units such as Genestealers which would normally be quite good against Marines in combat whilst thanks to a silly FAQ ruling,
And thus we get to the final advantage Grey Knights have - their Terminators (and Paladins). Here's how Tyranids deal with Terminators normally. Vanilla die in combat to MCs/Gribblies. TH/SS die in combat to Gribblies. GKT and Paladins combine the best of both worlds, having guns which hurt the big Tyranids and the little guys in equal measure and having the combat ability and number of attacks to tear both up in combat. Lash whips aren't helping against Halberds which are common on these guys and with a Brotherhood Banner, they auto-instant death your big Tyranids. With the lack of ranged anti-infantry firepower often available to Tyranids, these guys can hurt a lot.
Oh and before we forget - psychic defenses. Grey Knights will always have some to stop such powers as Paroxysm but will also regularly come with the ability to stop Catalyst and Onslaught. Not nice. And of course the usual advantage mech gives an army over full foot lists. This is less pronounced with Grey Knights as they use their mech to get to midfield then block/protect their infantry but those Razorbacks can still move around, tank shock you off objectives, disrupt your advance and find those hiding Hive Guard.
Tyranids - Advantages
This is bleak. A lot of normal Tyranid strengths have been nullified to an extent by Grey Knight special rules. They may still be strengths but they just aren't as strong as usual. Let's look at them.
Combat as always, is Tyranid's greatest strength. Unfortunately, with the combination of Nemesis Force Weapons, Sanctuary/cover, Halberds, Hammerhand and Cleansing Flame, well Tyranids find it hard to actually roll over these guys in combat like normal. The little guys can still do decently well against regular GKs since hey don't have counter attack (stay away Grand Masters!) but are often weakened by storm bolter fire en route and are striking last. Genestealers, Raveners and Warriors will still have lots of fun with most Grey Knight units however, especially if they can get clear assault lanes. The MCs of Tyranids are less effective than normal considering the mass of armor ignoring weapons, hammers and force weapons rolling around but will still generally beat squads handily - there's just the chance they may poof. Trygons and Hive Tyrants will still dominate most units as well.
The durability of Tyranids is also one of their major strengths which Grey Knights nullify to an extent. However, the lack of low AP weapons commonly seen in other armies means most of the Tyranids will get their save and FNP (if cast successfully) against most of the firepower coming in at them. Whilst Grey Knights can force a lot of wounds, 3+/4+ with six wounds is still hard to take down. As long as the Hive Guard are decently hidden so only a few if any units can shoot them, the durability of Tyranids can allow them to advance, fire and hopefully get into combat ASAP. Blocking FNP with a psychic hood however can greatly reduce these chances or if the Grey Knight player has brought along a lot of LasPlas RBacks which cannot be suppressed easily.
This leads us nicely into Tyranid saturation. Grey Knights have the tools to deal with every unit at range thanks to stormbolters, psycannons, psybacks and Psyfledreads. If the big Tyranids do survive however, there is some associated opportunity cost for Grey Knight shooting. If you're shooting at the big Tyranids, the little guys can swarm over your basic Grey Knights relatively easily (even if striking last) and if you shoot at the little gribblies, the big guys have the ability to dominate the game, especially with little AP1/2 shots. Of course, target priority against Tyranids is always pretty easy (shoot the big ones first) but there is some cost associated with this for Grey Knights when there firepower is all tied up in similar units.
Shadow in the Warp is probably one of the best things Tyranids have going for them against Grey Knights as well. It will stop a lot of psychic powers from even being attempted to cast as the Grey Knight player does not want their Justicars' heads to explode (and correspondingly higher Ld and often hammer wielders). This will obviously greatly increase the durability of MCs in combat as Force Weapons are less likely to get activated and improve the combat ability of the army overall as powers such as Sanctuary and Cleansing Flame are less likely to come into play. The downside of course is the range and that powers like Shrouding, Sanctuary, etc. can be cast from inside a transport (which SitW doesn't penetrate...go figure). If you are able to get SitW into the Grey Knight lines quickly with a Trygon or Shrikes however, all to the better but be careful you don't overextend.
And finally we get to anti-infantry. Tyranids generally have issues with ranged anti-infantry firepower (i.e. beyond 24") but most Grey Knight units need to get within that 24" to shoot you. This means if they can shoot you, the 18" blasts seen on the big Tyranids will be in range. Devilgaunts, Zoans and Biovores are also good choices in being able to put out lots of wounds on infantry within that range. This works particularly well against Grey Knights as they often fight outside of their transports. No longer do you have to rely upon breaking open tanks before throwing these types of firepower at them - they'll often get out to better shoot you.
Oh and as an aside - Paroxysm is great for dealing with Paladins and Terminators but with Aegis, Reinforced Aegis and psychic hoods, cannot be relied upon. When it is cast though, it is much easier to deal with those units compared to normal.
Conclusion
Grey Knights have the obvious advantage. Too many of their strengths weaken the strengths commonly associated with Tyranids such as combat, suppression fire and their durability and other strengths close in on Tyranid weaknesses. Whilst Tyranids have some effective tools against Grey Knights such as Shadow in the Warp and lots of anti-infantry potential which can reach the Grey Knight lines, they don't overcome the advantages Grey Knights already have.
Again, it's certainly not an auto-win for Grey Knights and like against Imperial Guard, if they big Tyranids can survive through T6/W6/3+/FNP for a length of time whilst the Hive Guard hide and pop tanks, you've got a game on your hands. That being said, Grey Knights do have the firepower to punch through those defensive stats whilst also having enough firepower to drop the little gribblies and T4/W3 Tyranids. Against Grey Knights it seems like less big creatures and more medium/little guys might be better but the more you cater to taking on Grey Knights, the harder it is to balance your force against other armies out there.