So, you mean your boyfriend just isn't that compatible with you?
I am the kind of person that wants strong, genuine, long-term commitment.
If I met someone else and felt I got along a lot better with them and was more generally compatible with them than my current boyfriend, then I would doubt whether I had made the right life choice in being with him. If the doubt was considerable enough to become a certainty that I would and could be better off with a different kind of person, then I would leave him.
I wouldn't go out with the other guy straight away though. That can be a mistake - jumping straight into another relationship when you didn't feel your first one was good enough. I would wait some weeks at least if not months depending on how serious my relationship was. I'd probably be getting to know the new guy more, letting the dust settle and thinking about everything to do with my previous relationship - whether I was wrong or right to leave it, positives and negatives, seeing how life is on my own without anyone else to get a better feel for how exactly I myself want to live. If I end up choosing to spend all my time with this new person though, that would be a sign - but I would hold back from getting romantically involved until I was sure they were right for me and it wasn't purely because I was used to having someone close out of habit. If they really suit me well and are looking for the same things I am (serious, longterm) they probably won't mind waiting, getting to know me more first too. If they walk away, aren't having as much fun with me as I am with them just because it's not yet intimate, I doubt they were right.
That's just me though, I take this kind of thing seriously because I'm in it for potentially a lifetime and don't want to mess around with anyone.
I would want to show my previous partner due respect, because there would have been a reason I got together with them - they wouldn't be a bad person, just not the right person for me to be with, so I would want them to understand that with all the reasons we weren't as compatible as I want so they can move on as healthily as possible. Not just think I 'upgraded' as soon as I could. I love and respect all people I feel like I know or have been drawn to before, basically, even if they do bad things or we need to part ways (I wouldn't expect this of people escaping abusive relationships, mind).
Not everyone is like me, I understand that. So it seems to me like what you are going to do instead is wait until this guy makes a move on you, or make a move on him, and only then leave your boyfriend.
It happens.
I wouldn't feel comfortable with someone who made a move on me while I was in a relationship, they would have gathered if they knew me at all that was a terrible idea against my values. It would rule them out for me, someone who would disrespect both me and someone I cared about. Other people don't feel it that way though.