I'd say AC wins, because I much rather the open-world experience compared to Prince of Persia's linear style. I'm not a big fan of PoP's combat system, just because button mashing isn't really my thing.
Prince of persia with no doubt, after all, prince of persia have a better sotry (in my oppinion) and I don't care a lot for graphic, because the real matter that we play a game is tree things, story - easy controls - cool movements
Assassin's creed. The Prince of Persia games are kind of redundent, and get borring after a while. AC has a much better story, and the graphics are better.
hrmm... I would have to say I prefer the AC games over the PoP games but not by much. I am probably the only person in existance that liked the newerish PoP (one before sands of time) everyone seems to hate it just because it's different... woop dee doo I liked it about the same as the previous games. (and don't lump the movie in with the games the franchises arn't being compared here) I don't really think the open worldness of AC is what makes me like it more though (im sure it is) I just loved the kill scenes :P but really all the open world aspect of the game did for me is make me have to walk that much further to continue the story... all you did otherwise was (for the second one atleast) collect the tokens for the armor or collect feathers... I liked the armor idea and enjoyed doing the little puzzles to get them but otherwise I didn't really care that it was open world.
AC has better movement and story. It is VERY much inspired by PoP but it doesnt stop being a better edition of the PoP! I used to be a fanatic fan(>.< of PoP, but by the time AC was made, things changed for me...