I've never had any success with the "lift/drop". I always drag. I will say that many, many jigs bites have come right when I pop the jig over something I drag it up against. Some of my biggest bass have grabbed my jig or t-rig when I drag it, drag it, drag it, and then have to pop it over an obstruction.
I did too until I changed my technique. I keep the rod mid-low and I drag the jig by pivoting left or right using my waist in a long, slow motion. IMO I can feel the bottom better doing it this way instead of the "low to high" rod motion. When I encounter an obstruction I'll turn back and face the target. I'll shake it a couple times and, if nothing, I'll pop it over the log or rock. This is where I've gotten a lot of good bites. Pivoting at the waist left or right helps me move slow and makes it easy to go smoothly or twitch the rod for little spurts of movement. Just find it easier to concentrate than the low-to-high stick for some reason. My own mental issues I suppose.