Which CPU: AMD phenom II x4 965BE or fx 4100

Absolutely a Phenom II is a better CPU all around. I'll take 4 real cores to 2 cores +2 pretenders any day.

The FX uses less power at stock clock rates, however they get very hungry when you start overclocking. Either way though, in terms of your electric bill, the wattage difference of CPUs is pretty insignificant.