Released in 2006, it is the third console that was released by Sony. When it first released, it had backwards compatibility for PS2 games with no problem. When Sony made the slim version they removed it and now are putting PS2 Classics in the Playstation Store. When the PS3 first released, Sony used a cheaper lead based thermal compound on their CPU and GPU. That was a problem because that paste could become brittle when heated. The CPU and GPU would them over-heat and cause what is called, the Yellow Light of Death (YLOD) which would render the system useless until repaired. The System uses an easy to understand X-Bar Menu (XMB) which puts every option into a place where you can see everything under easy to understand sections. The PS3 graphics differ between games. Most games though have 1080p. Most games don't differ from it's original 60 FPS and if they do, it's higher than 60 FPS. The PS3 controller features SIXAXIS technology which acts as a Wiimote. You may till it and it will move a certain part on a select games. Sony never differed from their original design for the PS.
Released in 2005, the XBOX 360 is Mircosoft's second console. The XBOX 360 had limited backwards compatibility. The 360 also had a system ending error that is similar to the PS3s YLOD except some of the problems could be fixed at home with no extra tools. Each ring on a 360 is different when it has the Red Ring of Death (RROD). Mircosoft released the 360 S with hopes that this problem will be fixed but, it wasn't. The 360 has a simple menu that was updated and became how Microsoft has Windows 8, smooth and clean. The 360 also stays at the 60 FPS and sometimes surpasses it as well like the PS3. The 360 controller was originally powered by AA batteries. They upgraded to charger battery packs.
Though both consoles are great and have their own flaws. You choose what you like and that is that. Nobody should try to convert someone to PS3, XBOX, or Wii. That person should make up their own mind and dislikes of it. I personally like PS3 just the fact that it is better in my eyes.