well as a start the biggest difference is in ranking.
hollows evolve to rank, and they have alot more freedom in evolving. whereas a shinigami can't have bankai at level 5, a hollow could become arrancar at level 1 (although if you did you'd be far weaker by the end of the evolution line)
also, while all shinigami PCs will be able to get shikai and bankai, not everyone will be able to get captain and lieutenant, and therefore alot of people would miss out on those boosts.
but hollows, the only limited spot is espada.
the next difference would be in stats. assuming the hollow character goes all thee way and becomes a vasto lord arrancar, they will be better stat wise, than a bankai shinigami, and about equal to a captain (thats assuming they aren't even espada). if the same arrancar was espada, he would have more stats than a captain of the same level.
But shinigami have more available earned techniques, that being the wide variety of kido spells, not to mention kido types. (binding/barrier, destruction and medical) as well as different elemental kido, then they have extra techniques such as shunko.
shinigami also get more powers, by 2.
so it's a question of extra stats vs extra skills, in terms of character creation.
in terms of story making.
shinigami, you are a military force, you can't just go to the world of the living whenever you like, and you can't kill other shinigami without punishment, (as in severe punishment)
hollows, you are less organised, take that as you will, can go the the real world whenever you like, can kill hollows whenever you like, in fact you can do almost anything, as long as you don't step on the worng espada's toes.