Same here - I have always sweated a great deal under the arms, so I use roll-on AP. However, there is a difference between that smell and out and out body odor. The smell of sweat doesn't travel, whereas I have literally been 'downwind' of people with B.O. and caught a solid whiff.
All I'm saying is, if you're having trouble with B.O., then deodorant or antiperspirant will really only mask the smell somewhat, and possibly not a lot. In all seriousness, if you have trouble with B.O. then you probably need to wash your clothes more often, or yourself more thoroughly.