I absolutely love to answer these questions!
Now, I'm going to go over EVERY fossil's role/how it's used most.
Omastar usually runs one of three roles: a Shell Smash set, a Choice Specs set, or a Suicide Lead set. The Shell Smash set, if under rain, can lead to easy sweeping. However, with permanent weather no longer being a thing, this set is on the downfall. The Choice Specs set packs an immense punch, being able to 2HKO Chansey after its Eviolite is gone. However, there's always the drawback of being locked into a move. And the suicide lead set just throws out hazards and dies. Due to many weaknesses like the ever common Fighting and Grass type, Omastar is down in RU.
Kabutops also runs one of three sets: a Rapid Spin set, a Swift Swim sweeper set (try saying that 5 times fast) or a Swords Dance set. Rapid Spin is an invaluable niche, and not many Pokemon get it. I actually run Kabutops on my RU team solely for Rapid Spin. With Swift Swim this thing becomes insanely fast, and with its high Attack and the rain boost to Water attacks, this thing's Waterfall is gonna hit like a truck.
252+ Atk Life Orb Kabutops Waterfall vs. 252 HP / 252+ Def Aegislash-Shield in Rain: 274-324 (164 - 194%) -- guaranteed OHKO
But again, due to its many weaknesses and the weather nerf, Kabutops is down in RU as well.
I'm starting to sound like a broken record, because this one also has three viable sets, that almost mimic those of Kabutops. In fact, Armaldo runs the same sets as Kabutops, except one thing: Armaldo is immeasurably slow. OK, maybe not THAT slow, but he is not the faster Pokemon around. With a pretty low SpDef and low Speed, he's really easy to revenge kill. Oh, and often, Armaldo runs a Choice Band over Swords Dance.
Cradily actually only has two viable sets I've seen- Stealth Rock and Curse. Cradily is also extremely slow, but has a better time of it because it can raise its lower Defense by using Curse. Cradily dies quite easily to Toxic stall, so status it and it is essentially out of the match.
Bastiodon's got one set and one set alone. Roar, Toxic, Stealth Rock, Magic Coat. Maybe Metal Burst. You see, Bastiodon's got great Defense and Special Defense, but every other stat is complete garbage! When you throw in a 4x Fighting weakness, it just makes this dinosaur even sadder.
Rampardos has... you guessed it, three viable sets! Rock Polish, Choice Band, and Life Orb. Rock Polish allows it to patch up its meager Speed and sweep with relative ease. (I'm just waiting for this thing to get Dragon Dance.) The Choice Band set hits like an absolute TRUCK, and Sheer Force Life Orb works well with its large movepool. But poor defenses and Speed hold Rampardos back from becoming amazing.
Carracosta runs one of two sets: Shell Smash or Stealth Rock. With its high defenses, Carracosta can shrug off the -1 in both and sweep with the massive boosts it's accumulated. That's why it's also a good Stealth Rocker: it tanks hits well and can give them back. But again... Speed.
WHY GAME FREAK WHY
Seriously, if not for Defeatist, Archeops would be one of the best Pokemon. High Attack, Special Attack, and Speed, in combination with a large movepool, allow it to run a lot of different sets. I've seen lead sets, Taunt sets, Mixed sets, Scarf sets, Band sets... Archeops is just a versatile Pokemon. But Defeatist is its downfall. Come on, Game Freak. You know you want to take Defeatist off of Mega Archeops.
Tyrantrum has insanely high Attack and Defense, and good Speed. But thankfully, it's got access to Dragon Dance, not to mention one of the best weapons in the game: a recoil-free Head Smash. A spammable base 150 power attack is fine by me, and after Dragon Dance, it's simply amazing.
Aurorus has high HP and meh everything else. It's got a great ability and move combo in Refrigerate + Tri Attack (Nature Power) but its low speed and weak typing leave much to be desired.
Aerodactyl and Mega Aerodactyl
Without a doubt, the best fossil in the game. Blisteringly fast, with high attack to compliment it, and a rather large movepool, including Aqua Tail and the elemental fangs. It's got good defenses, so it won't die if you poke it with a feather. The only bad thing is its lack of good Flying STAB.
Fossils aren't the most viable Pokemon. They're held back by a required Rock typing, which happens to be weak to the three most common priority moves (Bullet Punch, Aqua Jet, Mach Punch.) In addition, their low speed and somewhat shallow movepool keeps them from going far. Not a single one can boast that it's in OU, but the highest is Aerodactyl and its Mega up in UU.
Here are the fossils' highest stats:
Omastar: Defense and Special Attack
Kabutops: Attack and Defense
Armaldo: Attack and Defense
Cradily: Defense and Special Defense
Bastiodon: Defense and Soecial Defense
Rampardos: Attack (that's its only good stat)
Carracosta: Attack and Defense
Archeops: Attack and Speed
Tyrantrum: Attack and Defense
Aurorus: HP and Special Attack
Aerodactyl: Attack and Speed