Ooooh, as a Tyranid player and a huge Godzilla fan this is perfect for me! Okay, so this match up is fun, but is also basically "Goku vs Superman" in terms of the ludicrous feats on both sides. Ultimately, the no-fun-police answer is Godzilla because Toho has decreed he can't die and GW loves to see Nids defeated, haha.
But to play along with the hypotherical, kaiju films are one of the few mediums as ridiculous as 40k. Godzilla has some ludicrous durability and power.
At the base level, you have Big G's complete immunity to conventional weapons. How far does that extend to 40k weapons? Great question! A Tyranid fleshborer isn't exactly conventional, but it's also not a goddamn cruise missles or tank shells, and Godzilla completely ignores those. Heck, Godzilla doesn't even blink when taking point-blank barrages from the 16" main battle cannons on an Iowa-class battleship and those beasts fire shells that are 2,700lbs each. Those would take out a Space Marine if they could hit one. So it's hard to grade where a lot of Tyranid weaponry falls.
At the higher levels of weaponry Godzilla obviously tanks nukes (including the Castle Bravo blast that was the largest nuclear weapon ever built by the US irl). Of course, that's not entirely a fair comparison because he also absorbs radiation, so nukes technically are food to him.
There are some weapons in the Godzilla universe that are closer to the nonsense 40k throws around, though. Here are some that I think are fairly comparable.
MASER CANNONS:
Literally what it sounds like, a microwave laser. There are a ton of these used in Godzilla, especially in the Heisei series of films. They range from "small" tank-mounted versions, all the way up to the massive kaiju-mounted ones wielded by MechaGodzilla and M.O.G.U.E.R.A.
These are conceptually (and visually) equivalent to lascannons/turbolasers. Same basic idea, more or less the same mechanism. The smaller vehicle-mounted masers are barely more than an annoyance to kaiju. They've occassionally hurt weaker kaiju, but never Godzilla. The kaiju-mounted ones are powerful enough to at least cause Godzilla pain, but they are usually just the weapons used to keep him occupied long enough to charge whatever that movies super-weapon is. They aren't ever an existential threat to him.
PLASMA GRENADE:
This weapon is not a grenade. Please don't ask me to explain why it's called that. It's actually a massive plasma cannon mounted in MechaGodzilla's chest. Probably equivalent to plasma weaponry in 40k, and about the size of the ones mounted on 40k voidships. This one hurt Godzilla, knocking him over. Definitely a threat. Bio-plasma is also something Tyranids do a lot of.
DIMENSION TIDE:
This was a satelite that fired black holes in Godzilla vs Megaguirus. Godzilla was unfazed by thrm, but they also "only glanced him" with it and... like... how do you glance someone with a black hole? That's not how black holes work! Not something we've ever seen Tyranids do, but there are black hole guns in 40k. I think one of the pre-Great Crusade Mechanicus warships has one?
ABSOLUTE ZERO:
Another MechaGodzilla based weapon, this one from the Millenium series of films. A gun that fires a pulse that reduces the target to absolute zero temperature. So cold that atoms stop moving, destroying the target at the subatomic level. They didn't score a direct hit on the Big-G, but still managed to badly hurt him with it, leaving a noticeable scar on his chest (a feat almost nothing else could do). Again, not really something we see Tyranids do, but it feels very 40k. Feels like something a Necron Cryptek could pull off.
These are the most "40k" sounding weapons, so the best comparisons I have. I am leaving one out though, and it's a big advantage for the Tyranids. Godzilla's main weakness is electricity, which bypasses his naturally nigh-invulnerable skin to attack his central nervous system directly. It's never been shown to kill Godzilla, but it can stun him or even fully incapacitate him for awhile. This is fairly consistent across Godzilla films, and bio-electricity is something Tyranids use frequently.
(Edit: not as consistent as I'd like, as a commenter pointed out sometimes Godzilla can absorb electricity instead, but on-balance much more of a weakness than anything else.)
Given all of this, and given enough time, I think the Tyranids could eventually evolve enough to take out Godzilla. Bio-acid, psychic powers, they have a lot of different tools to play with, and the Hive Mind is a clever girl.
I'm not sure they'd have the time, though.
Godzilla isn't just a tank, he also puts out just as much power as he can take. More really. While the Showa-era Godzilla's atomic breath isn't particularly impressive by 40k standards, the Final Wars, Shin Godzilla, Minus One, and Monsterverse versions are stupidly overpowered. Monsterverse Big-G effortlessly bores a hole down to the centre of Earth with a single blast, and Shin Godzilla manages to flamebroil all of downtown Tokyo by accident just charging his blast up. Final Wars and Godzilla Earth have both shot alien warships out of orbit, which means even the Hive Ships aren't safe.
And that's just his atomic breath. Godzilla has pretty insane amount of powers, ranging from the stupid (flight in Godzilla vs Hedorah) to the amazing (complete and near-instant regeneration), to the God-like (literally he has just been a God at times, or in the case of Godzilla: Singular Point, some sort of eldritch abomination from beyond time and space).
Ultimately, this could go either way depending on the writer, how big the Tyranid fleet is, and which version of Godzilla. It was fun to think about though.
