The Definitive Editions are basically a remaster of the 3 games - higher res textures and models, updated lighting, general improvements, etc.

Rockstar/the studio they gave the project to botched the job pretty hard. Innumerable bugs and glitches, compilations of which can be found on YouTube.

In the 2 years they’ve worked on the Definitive Edition since release, they’ve tackled some bugs, but many still remain. I wouldn’t recommend paying for it yet if you want to try them, and instead stick with the original versions. The older versions might look dated but at least they aren’t a hot mess.