Drop-D has a great advantage for playing G chords, in that fretting G on the bottom string (5th fret) still allows you to get at D/G/B on the upper three strings (frets 7/8/7 respectively), which is very useful. If you're playing rhythm, it also gives you a very chunky chord from holding down 5th fret on bottom three strings (G/D/G).

Double drop-D (DADGBD) can be easier for D minor work, by making the D/E/F runs easily available on the top string.

It's all horses for course though. Usually you'll retune to put particular melody or harmony notes under your fingers more easily, and then it's trading off the ease of playing a particular chord against whether it affects how you'll play the rest of the song. I'm currently using open Gm7 (DGDGBbF) for one song - I'd never use it anywhere else, but for that one song it puts everything in exactly the right place.

Retuning shouldn't be a big problem with an electronic tuner and a non-floating-bridge guitar. If it is, maybe your nut slots are over-tight or your tuning machines are on the way out?

Graham.