i believe the 4100 and the 4300 are about the same price now
would be close between the phenom ii x4 and the fx 4300
but the phen iix4 would beat the 4100 but the 4300 mite pull ahead cos fx overclock to aroud 5ghz and the phenom around 4ghz
The Phenom II actually has four full cores whereas the FX doesn't. The FX is more power and thermally efficient, but the Phenom II happens to trade benchmarking blows with the FX while having a somewhat significantly lower native clock rate. And overclocking that thing to over 4 GHz can be done, usually, just by tweaking bus rates and not even messing with voltages. So it is a really harmless overclock, and really easy to do. Obviously though, the FX can also be overclocked. So it really depends on what you want. You can find the Phenom II X4 965BE for around $89 at the moment, so it is a very good price for the performance you can get out of it.
Alternately, if you look into the overclocking side of the world, you can actually get a Phenom II X6 1045T to around 3.4 GHz without having to change the core voltage simply by tweaking the bus rate and the two unlocked multipliers that you have for the Hyper Transport to system bus muliplier and the system bus to RAM clock rate multiplier. The last two you should lower if the final outcome winds up higher than the board natively supports, or the RAM natively supports. But those chips are selling for around $100 and have six real cores.
That is a pretty solid budget build.
i'de say don't go with the 4100, it has a few bugs. instead get something like the 4300, or 6300, or 8350 as the recent architecture revision has fixed a few problems. the fx chips are way more overclockable as well
please please please please please please don't buy a 4100, just save up a little longer and get a 6300. You'll thank me so much for that.