One can retrieve the processor support for ASUS M4A78 from the above link.
Both processors are mentioned there, but pay attention that as to Phenom II X4 965, it requires the PCB version at 1.02G of the same model mobo. You might need to open up the case and take a look at the mobo inside, and find the PCB version alongside the model number on the mainboard.
For the TDP of 95W or 125W, you might need to prepare a better heat sink for your system.
Athlon IIX4 640 (ADX640WFK42GM), 3.0GHz, 512KB, rev.C3,95W http://www.futuremark.com/hardware/cpu/AMD+Athlon+II+X4+640/review
2800 Futuremark Hardware
Phenom IIX4 965 (HDZ965FBK4DGM), 3.4GHz, 125W, rev.C3 AMD Phenom II X4 965 Review - Performance
3860 Futuremark Hardware
looks like the Phenom is the winner
The Phenom is more like an FX chip for power and cooling solutions, under 60C cooling solutions and a tdp of 125w
Athlon x4 max 70C and tdp of 95w
The Phenom II X4 965 is significantly better than the Athlon X4
I have one of the 965 CPU on my MSI 970A-G43 and it still is a viable CPU