What OS are you running on? I have version 9,10,11 12 and 13 installed on my Mac Book Pro and all run. on OS X 10.8.5. That stated, these days I run 11 occasionally and 12 and 13 most of the time. I have been able to have both 12 and 13 running at the same time.
I would check your hard disk to be sure that it is working properly. If it is failing it could be the root cause of the problem.
You say you removed FMS. FileMaker suggests that you not run FMP or FMP advanced on the FMS server. They prefer that you have a seperate development system.
I´m running OS 10.9.2. Must say it has lowered my MacBook Pro perfomance in general.
My hard drive seems to be working fine.
I will also check if FMS was unistalled correctly.
We have encountered an obscure crash with Mavericks Enhanced Dictation enabled.
Doesn't happen with the regular (web) dictation option in place.
So check that.
Otherwise, we don't have any crashes with FMPA 12 or 13.
Did you install any plugins and are they up to date?