LA 0 Centaur attempt.

[Eldariel]

Are both of you assuming that a centaur Barbarian 6 gets a full attack that looks like +6 Greatsword/+1 Greatsword/+6 Hoof?

No, +6 Greatsword/+1 Greatsword/+1 Hoof. However, Multiattack makes it +6 Greatsword/+1 Greatsword/+4 Hoof. That's just standard functioning of natural attacks; presently Centaurs get two Hooves and you can check their full attack entry for confirmation. Also, Hooves can be used to make attacks during Trample which is extremely useful, making Trample almost worth something sometimes.

But yeah, natural non-hand attacks are awesome; even Warforged's Slam kicks ass and it takes a handslot (on level 1, you can carry a heavy shield and use your Slam for damage given a high-Str type thus getting you 1.5x Str AND shield). The additional problem here is, of course, with just one natural attack the Centaur gets 1.5x Str on the Hoof-attack too. It definitely warrants spelling out that he only adds 1x Str on the Hoof-attack.