Most relationships go stale sooner or later, which is why it is so important to get to know someone properly and be confident it is going to work before making a long-term commitment.
I think it sounds like a wise decision to break up with your current boyfriend and move on to the next guy. If he’s helpful and caring, that’s a welcome improvement compared to a guy who is not interested.
Out of respect for your current guy (and to show your new guy that you don’t mistreat boyfriends), I believe you should break up before moving on.
It seems simple from what you’ve said. I suggest, "You seem disinterested, and I’m not happy with how things are going. So I believe we should break up now, before we get sick of each other."