I have not touched FMP in ages, but as far as I recall, the original(ish) commendations either did nothing or gave tiny amounts of bravery. Not seeing any soldier bonuses in FMP or FMPE, either. So, probably nothing.
If so, then basically all the commendations are is the glamorous part of your soldiers' record. With soldier diaries, there's a giant amount of information stored for each soldier, which you can see and reminisce about. Find your deadliest Muton killer, best sharpshooter, the guy with 300 missions in Antarctica, etc. Not that any of this protects these celebrity grunts from eating hot flaming plasma next mission.

X-Com Files, Piratez and probably a few others indeed give you stat bonuses for getting commendations. Quite a lot, too.
Also, isn't FMP on 3.3 now? And if OXCE crashes on you, the better course of action is to report it in the OXCE subforum, because at least for FMPE, nothing guarantees 6.6 will even remain compatible with future versions of the mod.