I would leave dinosaurs as beasts. When I first saw it I said it was wrong myself, but after consideration I have changed my mind
Beasts are defined as Non-historical, or Non-real world creatures.
Contrary to popular misconseption Dinosaurs are Non-Historical. Don't misunderstand me, I'm not saying they didn't exist, I'm saying they didn't exist in history. Remember History is only that period of time that humans have recorded, dinosaurs came before that. Passanger Pigeons and Dodo Birds are animals Dinosaurs and Sabertooth cats are Beasts.
As for the arguments that in a campaign world with dinos they become both historical and real world (in the context of that world) This is a good arguement, save for the fact that then so are orcs, and dragons, and demons and mind flayers all of them would be animals becuase they are historical and real to that world.
Finally, the best arguement for leaving them alone is simply, Beasts get better stats than animals, Dinosaurs were stated up to be more powerful than common animals, beasts are more powerful than common animals.