Hey, Tina,
I think it's great you're getting your boyfriend a drumset! It's a bit hard to answer your question without hearing the drums and cymbals and seeing the hardware, but here goes.
Neither of these drumsets are made anymore, and I don't know what kind of wood they're made of, so I can't tell you about the quality of the sound. But the
Mapex 16" floor Tom is a good size, while the
Yamaha 13" floor tom is pretty small in my opinion -- the 16" floor tom will have a lower pitch, and the floor tom is your lowest-pitched tom. The
Mapex 22" kick drum is a good size, and we don't know the size of the
Yamaha. I'd sure like to hear the snare drums, and all the drums, but given the information you have provided, I would choose the
Mapex drums.
As for cymbals, you get more and better quality, IMO, with the
Mapex kit. Cymbals, actually, are a matter of personal taste, but I'd choose four
Sabian and Zildian cymbals any day over two Solars. Also, the cymbal sizes are good with the
Mapex kit, and we don't know the cymbal sizes with the
Yamaha. You've also got cymbal stands for all the cymbals in the
Mapex kit, but you don't mention any with the
Yamaha kit.
New heads, a cymbal bag, and throne are nice items included in the
Mapex kit. They sound like they're worth more than the sticks, stick bag, and seat in the
Yamaha kit. (Again, it would be nice to see everything.)
I own two
Yamaha drumsets, a
Yamaha four-wheeler,
Yamaha motorcycle (formerly), and two
Yamaha keyboards, and I would choose the
Mapex kit for sure, based on your information. And I think it would be well worth paying the extra $100 for the
Mapex kit. Good cymbals cost a lot, as does hardware.
Don't know if you want to show your boyfriend both kits -- maybe he could play them and see which drums and cymbals sound best to him. But if that's not gonna happen, I think your decision's an easy one.
Good luck!