The 5160 has a 3Ghz clock vs a 2.4Ghz for the E6600. The 5160 also has a faster memory speed. The Core2 is 10 years old, the Xeon "only" 9 years old.
Only if you have a REALLY old system with no other options is either work messing with today.
It's tough to say because since they are both dual cores it really depends on your intentions. It's entirely possible that your intended use will be demanding enough that there is no real world performance difference between the two.
The 5160 is an LGA771 CPU. the E6600 is an LGA775. The Xeon swap doesn't work on all motherboards. If you have an LGA775 MB that supports 1333fsb then it probably supports 45nm CPUs and you should have better option there anyway. E8600, E7500 with tape mod to 3.66Ghz. Unlocked X6800 would be another 2 core 65nm option. If you said what MB you have we could give you more specific advice.