I am not nearly familiar enough with Naruto to make a call but:
Ichigo, Orihime, Chad, Ishida, and Kon would be pirates similar to the Straw Hats in terms of overall interaction and varied fighting styles - I'm not sure how they would compare in strength - Ichigo would definitely have a bounty.
Urahara and his shopkeepers would be wanted, but would be more like Arlong in that they camp out in one place, only they wouldn't be as cruel and sadistic as Arlong - they'd probably sell pirates and other criminals stuff like log poses or advice in their store. Alternatively, they could be viewed in a similar light to the way the Straw Hats relate to the Red Haired Pirates, with Urahara being the "Shanks" in this case.
Rukia would be something like a Vivi character as she is part of a noble house in the Shinigami world. Obviously most of the shinigami would be Marines. Soi Fon's divison would likely be somewhere in the Ciphel Pol division, but probably not CP9 level. Shinigami captains would likely be on-par with admirals like Aokoji and the vice-captains would be on-par with Vice Admiral. Hanatarou would be on-par with Koby and Helmeppo.
Aizen, Ichimaru, Tousen, and their hollow/shinigami cross-breeds would be like Baroque Works, with Aizen as a Crocodile-like character, Ichimaru as a Das Bones like character, and Tousen as a very serious Mr. 2 type character.
The Vizard would be. . . hmm. Good question. I'm going to say they would be another pirate crew, as they certainly don't seem like they would be Marines or normal every-day citizens.
I'm not saying they would replace these characters in the OP world, but this is how I think they would fall into place.