The latest Prince of Persia is re-telling the story with different image. Basically it's a reboot like Batman Begins for Batman movie. So they wanted to just name it Prince of Persia. I don't have problem with that.
About PS3 version, I thought it looked a bit washed up and a little blurry to cover jaggies. I got it for 360 instead.
PC screenshots looks beautiful as usual. I really like the art style. I was slightly worried after hearing they were going for cel shading but boy, I was wrong. They did a great job.