The most common, and generally most successful Tyranid build is T6 spam (I do not use spam derogatorily- I am all for using the most effective unit in every slot.), so I'll focus on that, but there really isn't a "majority" build for Daemons, so I'll analyze commonly used units, after the break.We'll start with the Daemons. Chariots of Tzeentch (a herald of tzeench with a chariot, bolt, We are Legion and Master of Sorcery) They can reliably put 1-2 wounds on T6/3+, between Bolt of Tzeentch and Daemonic Gaze. If all 4 fire on one, they could bring it down from 24" away, and being able to down a T6 MC every turn is pretty strong: Target priority is important, as you have to know which monstrous creatures need to go first: clever Tyranid players can manipulate and confuse target priority: what you want is every monstrous creature to have lost a wound or two, rather than all be unwounded and one dead.
Great Unclean Ones are devastatingly effective against other monstrous creatures: hitting on 3's and re-rolling 2's to wound is excellent, and they have 5 wounds and, more importantly, a 4++ to defend them from other Monstrous Creatures. A Daemon player will want to get it in combat with key Monstrous Creatures, but it's slow speed makes it easy to avoid and throw an alternate unit at it. Hormagaunts with Poison are brutally effective at killing them: about 20 can kill one in 2 turns of combat, and take 3 or so casualties back.
Actually, Poisoned Hormagaunts are a pretty good solution to most Daemon units: they're fast enough to catch even a Tzeentch Chariot, do insane damage on the charge, and strike before everything but slaanesh. Overkill is good here: if something like bloodcrushers gets to attack back, they can easily wound them and force No Retreat! wounds, killing the hormagaunts by the dozens.
Tervigons are a good choice for Tyranids. The ability to create free, throwaway units is fantastic, and they can be used to tie dangerous enemies for the duration of the game: use them to assault Soul Grinders, Great Unclean Ones, Tzeentch Chariots, Daemon Princes: any one-model threat will be silenced by a 10-14 squad of termagaunts. Bloodletters and bloodcrushers, however, will destroy the unit in one turn and attack the tervigon that spawned them.
Bloodcrushers in general will be a problem for Tyranids, but there are ways of dealing with them. Massed termagaunt shooting will kill them, especially from Devourer Termagaunts. Two Monstrous Creatures will kill a 3-4 man squad in assault, but be warned- the Monstrous Creatures will take a few wounds.
Hive Guard, a common unit in Tyranid lists, will find a role against daemons. They can force saves on Daemons from outside line of sight, putting wounds on key models. They won't kill anything by themselves, but the added wounds will be appreciated.
That's all I got at the moment. I think it's a pretty even match: the Tyranid's ability to bring so many bodies, T6 and otherwise, is a great advantage, but Daemon's eternal warrior and specifically their invulnerables help them stand their ground, making their lower model count work for them.
Oh, but an Epidemius list kills Tyranids. Period.
Thanks for reading!