My take on them from playing various versions:
General: The PR's music is the best of any versions. Graphics are the best of any non-PSP versions. QoL is better than most versions (or 2nd best in some cases). No extras from the PSP/DS/GBA versions or FMVs from the (load-time-riddled) PS1 versions.
FF1: One of the best versions, but lacks the extras from the PSP & GBA versions (all 3 have different art styles, too, though PSP is a hi-res version of GBA, while PR is a 16-bit-esque version of NES). Uses the magic charge system from the original release instead of MP, which isn't as bad as some think it is. Worth a playthrough just to see the original playstyle and artstyle modernized.
Ranking: S-tier - PSP; A-tier - PR; B-tier - GBA; C-tier - NES/FC; D-tier - PS1; F-tier - WS & MSX2
FF2: Best in terms of gameplay (fixed a lot of issues that plagued it since the FC), but 2nd for story. Same artstyle and extras issues as FF1. Play it if you want to avoid frustration in play and are fine with only the original story, but go with PSP if you want the extended story and can handle the weird leveling system.
Ranking: A-tier - PSP & PR; B-tier - GBA; C-tier - NES/FC; D-tier - PS1; F-tier - WS
FF3: The definitive version. It loses some minor extras from the DS/PSP version, but nothing that negates the value of PR's gameplay improvements. DS/PSP alters the story mildly, too (main characters get names, personalities, and cut scenes not in the original FC version). They are also in (dated) 3D graphics, which look grey and bland next to the PR's brighter, fresher looking 2D.
Ranking: S-tier - PR; A-tier - PSP; B-tier - DS; C-tier - FC
FF4: If you are a stickler for SNES-style graphics, this is the best. However, if you prefer high-res graphics, go with the PSP. Again, no extras from the PSP/GBA or DS versions. The DS version is practically a different beast in terms of graphics (dated 3D, though not as bland as FF3), translation (super accurate, but super wordy), and extras (weird New Game+ mode). Also notable, PR has the best version of the last boss battle music.
Ranking: S-tier - PSP; A-tier - PR & DS; B-tier - MSU-1 (J Hard Type w/ PR music); C-tier - GBA; D-tier - SFC; E-tier - SNES; F-tier - PS1, & WS
FF5: Practically the best despite a lack of extras. GBA version has more job classes, which is fine for a replay; beware the GBA's poor sound quality, though.
Ranking: S-tier - PR; A-tier - MSU-1 (Pixel Freemaster); B-tier - GBA; C-tier - SFC; F-tier - PS1
FF6: Another definitive version. Still missing GBA extras, but they are so-so anyways. PR soundtrack is notably even better than other entries in the series. SNES versions are good, but be wary of glitches (some of which can erase game saves) on any non-patched copies. PS1 has interesting FMVs, but otherwise not worth it.
Ranking: S-tier - PR; A-tier - MSU-1 (Pixel Freemaster w/ bug fixes); B-tier - GBA; C-tier - SNES/SFC; D-tier - PS1