There are a lot of benefits with a cheaper processor that doesn't overheat as much. However, if the cheap is made too cheap it could actually be weaker than the original. Imagine games like MGS4 only working on the original PS3 processors, on the new weaker chip the game crashes at key scenes.
In Xeno Saga, when Namco made the game for the new PS2's. Anyone with an original PS2 like me can't play the game without it crashing. They never fixed the flaw. The only option for me is to buy a new PS2 or play Xeno Saga on another newer PS2.