They are both obtrusive and I guess it would have to depend on how strong it is. I have probably had more experience dealing with people with bad breath than body odor. Both can be a sign of a more significant health problem, but sometimes it's is just because of something they have eaten. If someone has bad breath because they have just eaten an onion. I'm going to offer them a mint. Although some people have gingivitis and they know it so pointing it out would just embarrass them because until something done via the dentist, there is just nothing they can do. Body odor can also be attributed to medicines or medical problems, and sometime just too much garlic or drinking alcohol (bad breath can also be from drinking) or like
rorshak sobchak says they could be depressed and not bathing. This being said, both are offensive, but beware of the reason for the odor.