In terms of power, the PS3 is over twice as powerful as the 360, the ps3 has 9 cores, not one (8 SPE's and 1 PPE) while the 360 has 3 cores. The PS3 can also render textures just as well or even better than the xbox 360, as it can pool the Cell Processor's RAM into the RSX GPU.
Speaking of technical prowess, the PS3 is the best in terms of shading, lighting, and overall processing. (that means in every subject) The xbox 360 is basically running on only general purpose processing, which is fine for an OS or basic programs, but when it comes down to rendering CGI in real time, the 360 can't do that, ONLY the Playstation 3 can.
Anyways, as far as games go, the PS3 has a much more diverse library in the near future than the 360 does. Most of the xbox 360's major titles are shooters, while the PS3 focuses more on RPG's and action adventure. Such games coming only for the PS3 are Metal Gear Solid 4, Final Fantasy XIII, Uncharted Drakes Fortune, LittleBigPlanet, Haze, Final Fantasy Versus XIII, White Knight Story, Heavy Rain, Afrika, etc.
Want Features? the ps3 has them-
*Blu Ray- The next generation disc medium which can store up to 50GB (100GB in experimental models) The extra space allows game developers to make large responsive environments, complex artificial intelegance, HD video and audio, etc. without compression. (the xbox 360 only uses DVD which has a maximum capacity of 8.5GB.)
*Other operating systems- The ps3 can get different operating systems installed, such as Linux, allowing it to be an alternative computer, and you can install many diferent programs.
*Web browser- The ps3 has a decent web browser, which you can go to many different web sites with, it does have basic flash updates, but it does need to be improved upon, including in java, though this can be fixed easily via a firmware upgrade. Many popular sites like myspace and youtube are accessable though.
*Play TV- Pretty much Tivo for your ps3, a tuner that you can record things with. Though it has only been announced to launch in Europe so far.
*Interchangeable hard drive- This pretty much means you can change the size of your hard drive with any hard drive so you can store more things.
*Built in wifi- With the xbox 360 you have to buy a wifi adapter for $100, this comes standard in the PS3.
*Free Online- Self Described.
*Playstation Home- Playstation home is an interactive community of ps3 users where you can play games or meet up with friends and hang out at your virtual home and hang outs, as well as stream live media(releasing early 2008, and is FREE)