Posey is much more important than House. Sure, they both hustled, but Posey hit more clutch shots and came up with more big rebounds and steals than House. Furthermore, it'd be tough to find someone with Posey's size. While you don't love him at the 4, it's nice that at 6-8, he can guard practically anyone on the floor.
With House, while I wouldn't be opposed to having him come back, there's other knock down shooters that can be found. Furthermore, while I appreciated his efforts, there's no denying that he's not a point guard. Now that we have the proverbial bullseye on our chests this year, I wouldn't be surprised to see teams look to pressure him more, forcing Pierce or Allen to handle the ball. And if House is then going to just be a shooting guard, we might as well get someone like Brent Barry who can knock down shots and actually has the size of a shooting guard (not to mention better PG skills).