Most codices field monstrous creatures as a support element: Dark Eldar get the insane Talos, Eldar can field Wraithlords and the Avatar, and the chaos books field Daemon Princes.
With the Tyranids, though, there are no vehicles: there are merely monstrous creatures. As such, monstrous creatures fulfill the same role as tans. The chief advantage of the monstrous creature is that while vehicles have excellent durability from the damage chart, monstrous creatures have greater stamina in terms of doing damage.
A Matter of Wounds
I'm going to be arbitrary here, and take a hive tyrant with a pair of devourerers and a heavy venom cannon. Place it opposite a Space Marine Predator toting Heavy Bolter sponsons and an autocannon.
Aside from range, they're roughly similar in terms of guns: anti-personnel suite, and a weapon suitable for attacking lighter armor and heavier infantry. Following me so far? Have the image of a happy little hive tyrant, and our stout, chugging Predator?
Now fire a meltagun at them from within 6". Let's assume it hits, and neither of them have cover.
The Predator might:
1) be stunned, and unable to move/shoot for the next turn
2) lose a weapon
3) be immobilized
4) be destroyed
5) Explode violently, sending shrapnel and chunks of space marines into innocent bystanders
The Hive Tyrant might:
1) Lose a wound
2) Die, if that was its last wound
Capabilities, and loss thereof
Every roll on the vehicle damage chart has a 33% chance of temporarily inconveniencing a vehicle, 33% chance of degrading its capabilities permanently, and 33% chance of killing it outright. The exact numbers change depending on the AP value of the weapon.
Additionally, some vehicles may have an immunity to shaken/stunned, and while that's annoying as all get-out (...nothing like getting shaken/stunned results against Soul Grinders and Defilers, lemme tell ya) it's not that common, and even with extra armor, you can keep vehicles from shooting for a turn.
What does this mean? It means that even if you don't kill a vehicle, you can reduce its ability to participate in the fight, sometimes in a significant manner.
What use is a Land Raider Redeemer that's immobilized on turn one?
How's an immobilized Wave Serpent going flat out going to land? [Hint: not very well]
What use is a Hammerhead without its Rail Gun?
How's that Dreadnought going to do in assault without its Dreadnought Close Combat Weapon?
What's a stunned vehicle going to do when there are powerfists nearby?
How's a Leman Russ Demolisher feel when you forcibly removed its battle cannon?
Sometimes, even shaking or stunning is enough. If you shake something like a Hammerhead or a Leman Russ Demolisher, you've kept an expensive gun from contributing to the battle for a turn, and that may buy you some breathing room you desparately needed.
Stunning a tank near assault troops can sometimes be very unhealthy for a tank; S6+ attacks against the rear armor of 10 are...painful...en mass.
The Flip Side
So, just how do you lock a monstrous creature's guns down, or hold it in place? Oh, and for fun, realize that a monstrous creature can move and fire two guns, regardless of strength or class, and how this doesn't always hold true for vehicles*.
Sure, the Wraithlord has S10, ignores armor saves, and all that good stuff. He also has...2 attacks. So he got charged by 20 termagants that have Synapse support. So, Mr. Wraithlord, what're you doing for the rest of the game? That's right, squishing a gaunt a turn. Real productive, that. Bet you wish you were firing those heavy weapons, or wandering around flaming things, or insta-gibbing stuff like Warriors. But, you're NOT. You're playing patty-cake with largely inconsequential troops.
Also, cry if the other guy has lots of poison attacks. Your expensive T5-6 just got negated. Wraithlords HATE poison...
The downside is that a monstrous creature has two settings in melee: full blast, and d-e-a-d dead. That Trygon that's in a fistfight with you? Yeah, he's swinging all those attacks until you drop him, as opposed to, say, a Dreadnought. Mr. Dreadnought is big and bad and crushing you with S10 power weapon attacks until, y'know, someone with a powerfist breaks that dread CCW off. Then the dreadnought tends to go bye bye.
Cons of being a monstrous creature
While you're not going to lose combat capability each time you get wounded, you ARE still vulnerable to anti-tank weapons. As a slight con, melta weapons don't care about getting within half range of you, since S8 is S8 at all ranges.
Cover is harder to find, too. It's not impossible, but Vendettas are a royal pain for you.
Cover is not always enough, though. Toughness means that even small arms are a (small) threat to you. Bolters will NEVER harm a Rhino's front/side AV11; but bolters CAN wound T5-6. T5 monstrous creatures feel this keenly, which means stuff like Daemon Princes and the Harpy. 5+ to wound isn't bad if there are 6-10 shots like that, or enough melee attacks. However, T6+ ones tend to worry much less, but a 1/6 chance to wound isn't the same as 'Cannot Be Damaged'.
Even though you ignore armor saves in assault, monstrous creatures not inclined towards close combat CAN be tied up by large numbers of expendable troops. Furthermore, larger squads with a powerfist in them can kill you (...albeit, at a cost to themselves, BUT 4-6 marines are usually a decent trade for a monstrous creature).
Monstrous creatures that want to get into assault may have problems as you are slow, unless you have wings or deep strike (or deep strike WITH your wings). Deep striking into assault range also carries the issue of sitting there and bellowing 'SHOOT MEEEE' to the other army, which is something you have to work around.**
Monstrous creatures with guns tend not to have the same level of firepower as a vehicle. This is likely to balance out the fact it's harder to stop them from shooting.
Speaking of vehicles, vehicles can simply tank-shock troops off an objective. Even if they pass that morale check, the people move aside. If a monstrous creature wants to pull that trick off, you're hoping for an assault that leaves you within 3" of the objective to contest (or just, y'know, killing the guys...). Furthermore, monstrous creatures are technically vulnerable to tank shock. You get one attack against the front armor, and if you're one of the lower-strength monstrous creatures, the odds get a little long against toughter targets. Plus, you have to STOP the thing, so even if you penetrate, it's a 50/50 shot that you'll stop/kill the thing. Or, you just got run over, good job...
I think with Tyranids coming out, it's worth noting the differences between vehicles and monstrous creatures, since the Tyranids can and do press monstrous creatures into service as gun platforms.
1) Monstrous creatures fight at full strength until death***; vehicles can die in a single hit or lose weapons/mobility temporarily or permanently
2) Monstrous creatures can always move and shoot two guns; moving vehicles can limit their available firepower
3) Monstrous creatures are generally slower than vehicles, but see item 2 for the compensation.
4) Monstrous creatures can be locked in assault, for better or worse.
I think that wraps it up for the major ones. I think the MCs have more combat stamina because they're based on wounds, though this can be a double-edged sword.
*Mr. Predator is sad. When he drives, he can fire ONE gun, while the tyrant can stomp around all day firing every gun it holds. Mr. Predator thinks that makes the Tyrant intolerably arrogant. So, the Tyrant kicked the predator over.
**I'd suggest giving them lots of scary targets and asking if they can kill them all.
***Which may be Instant Death, in some cases. OR poison.