is tutoree a word ? i've always thought it was tutee

If he is not doing the work himself I don't see why you can't revoke that agreement to guide him, on the basis that you can't do it for him and he isn't living up to his half of the deal.
It's one thing if he was not too bright and struggling, it's another to make excuses instead of actually working.

I understand your concern and sympathize, but as you frame the issue it sounds like you HAVE been outgoing and involved with both students. The problem is while one student has responded to your guidance, the other hasn't so there is no need to feel badly or guilty.

I'm not sure if this is possible at your level, but can you suggest that perhaps he/she would work better with another adviser? I know with a thesis these issues can be tricky but if you frame it as "I don't think I'm the best person to help you, but X,Y, or Z would be better equipped to guide your work" would that work?

I do hope this works out for the best as I know how can frustrating it can be when I seem more invested in a student's work than the student is.

I teach a weekly class where they're both students, so I see them often, and one or the other stays after class every other week or so to talk about his thesis, so the problem is not lack of time spent with the problematic one.
It's not really that he doesn't care or try, it's just that he doesn't really understand the topics he's dealing with and is not a very clear thinker or communicator, so he makes very little headway.
I attended a presentation by each one last week, and tutoree A (the good one) was smart and concise, whereas tutoree B (the not so good one) was confused and jargony.
One self-centered reason I don't like this is because I'm one of the few "digital" professors, teaching programming and procedural modeling, etc., and we are seen by our peers as a little bit out there. It would not help my cause to be seen to have a student who tries to do a "digital" thesis without really understanding the underlying concepts, techniques or language.
Feel bad about bailing on him, though.