a) they only update character models and menu screens. The backgrounds aren't changed, only filtered at best resulting in a big clash in quality.
b) the original is extremely poorly coded on the PC and is basically half emulated or something. Getting it to run on newer systems even with mods seems to be a pain in the ass.
c) The HD menus from the mod have some very bad design and look like a bad RPG-Maker menu.
The re-release has some basic filters and stuff and allows higher resolutions resulting in mainly better looking 3D models. I think they changed some stuff so that modding isn't possible now until someone finds a way and updates the mods.
The best version would be the PS1 version on EPSXE with the right plugins but you ruled that out.
So its mainly a choice between ease of use and modding options.