Each album is not just remastered, but remixed, and that's a practice I do have some issues with. The earlier releases benefit the most, because the sound is cleaned up a lot and you can hear of lot of subtlety you just couldn't hear before. When they're strumming two 12-strings and a six-string (Banks played guitar on the earlier albums) they blend into a nice backdrop for the vocals and/or flute. Now you can clearly hear each part. The magic isn't removed or anything, and in some ways it even emphasizes the mastery these guys had at laying down patterns. Also, I only have ancient vinyl editions, or first-run CDs, of the Gabriel-era stuff. When I listen to the new mixes, it's not clear whether I'm hearing new things because everything's so much cleaner, or because he's messed with the mix. Overall, I like the first box. These albums have definitely never sounded better.
On the other hand, there are places where it seems Nick Davis said "I've always liked this riff; now is my chance to make it louder!" On some of the later stuff, there seems to be overcompression, and that's just bad. The idea that some parts are supposed to be quieter than others, as an artistic decision, is often lost since everything is now clearer and pushed to 10. There are some great riffs and licks that are meant to be countermelodies and support, but now they're up front, and I think that's a mistake. Genesis, at least up through the 70's, achieved a great sound by layering the parts, but not all parts had, or were supposed to have, equal volume.
Tony Banks approved the remixes, so Nick doesn't get all the blame/credit for this. But while Tony obviously had a hand in creating the original music, it's possible that these mixes sound better to his ears just because they're a new take on work he did 30 or more years ago. Sometimes just being different is better.
But the best news of all is that every album now has a 5.1 mix, which obviously provides greater separation of the soundstage and makes it even easier to hear individual parts. I didn't know that about the Grammy nod, but it's not surprising. A lot of work went into these mixes, and they do sound great. Most albums have a number of video features as well. Lost or rare concert footage, original videos, that kind of thing. If you're a fan, these are at the very least quite interesting to watch.