The difference is that a relationship is a type of agreement. Unless you're in an open relationship, part of that agreement is to not fool about with other people. No one enjoys break ups, but most relationships end. That's just a fact. Just because some people take them poorly doesn't mean that breaking up is worse than cheating. Anyone who would rather be cheated on that broken up with needs to grow a spine and find some self respect.
This whole "I met someone better" attitude you keep mentioning is pretty juvenile, to be honest. It isn't about finding someone "better", it's about finding someone more compatible. I don't recall anyone saying breaking up and then screwing someone else an hour later was a GOOD thing, but at least by breaking up you're no longer bound by the unspoken rules of the relationship.
Cheaters are indeed weak in that they either fail to live up to one of the most basic expectations of a relationship or just don't have the guts to break up and move on.