re: Taylor 110e vs Martin DX1AE

My experience (YMMV) having owned both a Martin (DC16R-GTE) and a couple of Taylors (210 and GS Mini mahogany)...
The Martin had to be played kind of hard to open up the sound, played a little stiffer and if you left it in the case too long, it let you know you had ignored it when you picked it back up. You have to play it pretty regularly to keep your chops up.
The Taylors are brighter and can be played with a lighter touch, in fact they don't seem to like the heavy hand a Martin does. Easier to put down for a few days and pick right back up again. More comfortable at first touch.
So, if you don't mind working a little harder, the Martin will reward you with more volume and a better sound (in my opinion.) This is just based on my own experience with the models listed, I don't know much about the DX.