I am adding my 2 cents in here..I have both!! I have had Fibro 16 yrs. and was DX. with RRMS 2 yrs ago, I am on Copaxone shots for the MS and nothing much helps the Fibro and have been in a very painful flair in my ribcage for the past 2 weeks that won't let up and it leaves me pretty much laying down with heat most of the time.I can't take any meds stronger then Tylenol for the FM as I also have Lupus Antianticuagulant a clotting disorder and I have to take a blood thinner so NISAIDS doin't mix well.
I guess I think the FM is worse 16 yrs. and counting and its still a mystery today as it was back then and a lot more painful, but the MS has its bad days too.
Thanks for letting me share.