Agreed, the i3 6100 has better multi-threaded performance than the FX-6300 despite having fewer cores. The FX is simply not a competitive choice anymore, unless you can find a screaming deal on it.
The i3 6100 is a better choice than the i5. They'll trade blows, but the i3 is new and a board for it will have new features and connectivity, and a warranty.
Some other contenders:
Pentium G4560 - basically an i3, 2c4t, and only $65
i3 7100 - same price as the 6100 but faster