There's no difference in how I ascend, descend, tend slack, or move in the tree DdRT or SRT. What's different is 1:1 vs. 2:1 motion while moving up the rope and multiple redirects available SRT to increase horizontal range and load sharing on the anchor.
I'm stating the obvious but I don't believe that SRT with the new devices inherently makes a person a more "natural" climber on the tree. However if you're already good on the tree, SRT is going to open things up quite a bit. Gear has never made the climber and it never will. Smart gear use can make a climber more efficient and safer, no guarantees though.
Speaking of which a climber who mentored me when I was starting out taught me something he learned from an old-timer, maybe this is common knowledge, don't know, works well SRT or DdRT ;-)
The arm lanyard. There are four ways to deploy your arm as a lanyard, from strongest to weakest:
1. Arm over branch up to your shoulder, resting on your armpit, very strong, very stable, hands free
2. Crook of your elbow around a spar or branch, what I use most often besides a hand grab, very stable position, hands free
3. Crook of your wrist, a strong hold, leaves your fingers free for a task
4. Hand grab on a branch, most useful, very effective for quick moves but weakest of the four
Disclaimer: this assumes all your arm parts are working pretty well ;-)
-AJ