In my experience, GDAE is the tuning to use if you want to play the tunes (i.e. the melody), GDAD if you are going to play accompaniment. To a great extent, GDAD is for the bouzouki player what DADGAD is for the guitarist.

My bouzouki teacher used to play tuned GDAD, and would capo at the seventh fret when he wanted to play melody. This never worked well for me since I found the frets to be too close together up there on the neck to play effectively, but my teacher was (and is) a much more skilled player than I. For mandolin players, the close frets would probably feel just fine.

I never had much luck using a capo "on the fly", so I played all keys without a capo. Key of G worked almost as well as D, though key of A was rather limited for me. This was Irish dance music, so I didn't have to play in "exotic" keys.

Don