My thoughts:
I really enjoyed PoP, especially the twist at the end. It definately leaves room for a sequel. Elika was alright, although I didn't really like the fact that you cannot die. Combat was pretty basic, but PoP games have never been very combat focused (with the exception of the Warrior Within, which I didn't like very much). The acrobatics were pretty slick, although they didn't feel as streamlined/quick as they did in the Sands of Time series. Maybe they made them a little more realistic, I'm not sure, but I like the much faster pace of the other games more.
Being an achievement finder they could have made the achievmets for this game SO much better. I HATED the "be gentle with her" achievement. This is one of the worst ideas ever, because it made people like me quit out of the game every time she saved me. There's no "load game" option while your playing, so I'd quit to the menu and reloaded. I bet that at the end of the game she only saved me 15 times...but mentally I couldn't keep count so I played it safe.
Prince of Persia games have never been about combat, they've always been about navigating obsticles, and with Sands of Time that turned into "navigating obsticles using acrobatics at very high speeds." My favorite achievements on this game were the "runner" achievements, they need to ditch the light seeds, the combat, etc achievements and make 20-30 "runner" achievements. Make some of them extremely difficult, that will make the veterans want to keep playing. And to top it off do what Devil May Cry 4 and Ninja Gaiden 2 (and other games) did, add "Time Attack" leaderboards for these running achievements.
Overall I'd give it a solid 8-8.5, I really liked the game although it has some faults and it doesn't really give the user a reason to come back and play it again. There is some DLC coming soon that will add new areas, but I don't know if it'll be worth the purchase.