I've already got 3.0.1.17, what does 3.4.0 have that the older one doesn't?

Bug fixes and all. I don't have a link but you should check patchnotes if you ar interested.

Bottom line : the launcher propose you to install the patches relatively automatically if that's your concern.

There were some important bug fixes in 3.1, and 3.2 made the "A Better UI" mod an official part of the game. Everybody should update through these.

There's a patch for Korean and Brazilian Portuguese text. There's also a patch that fixes some Chinese translations.

3.3 has improved controller support, and shrines that enhance the Aard and Quen signs.

3.4 is support for Redkit mods. If you want to play with the FCR 2 mod, you need to update to 3.4.