hehe i don't know what to say on this one, except your strings are old on the GS, or that the mini is easier to play.
tone is subjective, maybe you just like the mini better, that's a lot easier on the wallet!
maybe the gs is more responsive to you? i have 12 fret GC that is more responsive (plays with a lighter touch) but when driven hard, my GA's are noticeably louder
and with solid tops, there are variations, but yes, a GS and GA should fed sound more full than a gs mini, quite eqsily