I tend to use the former spelling because I'm lazy.
Okay, the serious answer is I tend to use the direct spelling from the official source. I don't know if it's correct (probably not), but if Tsuburaya is calling this ultraman "Mebius" on the official site, Mebius it is for me.
(Not sure why I never said anything about this before. Probably because it is no big deal. Spell his name any way (generic) you like; as long as I figure out we're talking about the same person, I'm good.)
Speaking of which, I contradict myself. Mebius
' Ryuu's name is spelled officially with only one 'u', and I did spell his name like that before. But I'm too used to writing "Ryuu" now that it's hard for me to go back. (And I have to put something over that single 'u' anyhow, to be absolutely correct. Or maybe (actually unlikely) I put in that extra 'u' to differentiate between this Ryuu and the one from Den-O...)
Anyway, the only consistent thing out of what I've said is that I'm not very consistent. You can find me write "Moebius" at least a few times too (in the icon keyword, mostly). I'm flexible and go for whichever spelling I feel like at the moment.
Okay, useless rambling over. I hope I don't make one of these boring spelling posts again in any foreseeable future.