I've done a pretty comprehensive comparison between the H3 and FX850 a couple of months back on this forum. You can try looking for it.
To get to the point though, the FX850 has harder hitting bass, better control and is more prominent compared to the H3, definitely bass heavy. The H3 can reach a bit deeper in the subbass region and has longer bass note decay (as expected with the 13mm sub-woofer) but that's about it, the lacks of impact and control is quite a disadvantage (even with the tape mod). The FX850 wins hands down in the bass department, imho. The FX850 WILL sounds bass heavy at first, but is tamed down over time as your ears get used to it.
Also, the FX850's mids are more forward and the treble extends more compared to the H3 too. The H3 has better separations and speed (also, as expected of the BA drivers). As result, the H3 sounds too mellow and too clinical for my taste. I'm into more "fun" sounding phones while still having that high resolution quality to it.
For me, the only logical and sensible choice would be the FX850.