groze: No, the PC versions of the Legend trilogy are all exactly the same as they had always been. GOG's versions come with the latest official patches that the Steam versions also have had for more than ten years, but that's it. If you own the Xbox 360 versions, your best choice to play these games is still via the 360.
I did get them all because, I mean, 6€ for the LAU trilogy AND the 2013 reboot was too good a deal for me to pass, plus, I don't even own an Xbox 360. Also, all these versions are 100% DRM-free, so there's that, too.
For the record, people shouldn't expect GOG to fix more "modern" games. GOG usually gets really old games to run on contemporary hardware and software, and I do thank them for that, but these games (supposedly) run on modern PCs out of the box, so, there's nothing for GOG to fix, really. I also wouldn't think Square-Enix would allow GOG to just mess around with their more recent games, because of breach of trust, contracts, NDAs, agreements, all that corporate BS that allows GOG to keep getting and selling games from all these different publishers. If anyone could fix Tomb Raider Legend, Anniversary and Underworld, it would be Eidos/Square-Enix, not GOG. Just my two cents, I understand why some people are kind of mad that GOG didn't "fix these games", but I don't think it should be GOG's work to do that.
Anyway, bottom line is: if you don't feel like getting the Legend trilogy because you have the Xbox 360 versions, then don't, as you definitely own the superior versions -- Legend and Anniversary, on the PC, are basically PS2 ports, whereas the 360 versions do have substancial graphical improvements, plus exclusive DLC the PC versions never got. It's up to you, really.
You don't need to have an Xbox 360. The game is backwards compatible, so you can play on both Xbox One and Xbox Series S / X.