I've been wrapping for a while and back carry daily. I notice I get sore after using any carry with ruck straps and I even question if they trigger my migraines. I've never tried a mei tai (except one I made for my first son that I didn't size very well) and wonder if those straps feel similar to rucksack straps?
My shoulders start to hurt after awhile when using ruck straps with a wrap. I've used a mei tai and an ergo and not had that problem. With a wrap you have to make sure the tension is even across the wrap and there is no padding. With a mei tai it's padded and the tension is sort of set as you can't adjust the rails and centre of the shoulder strap like you can a wrap, the tension is more even across the shoulder strap with a mei tai all on it's own if that makes any sense.
A mei tai will distribute the weight a bit differently than a ruck does. I still find wraps to be more comfortable for back carries. Depending on how long your wrap is you could still make it work for you.. I don't care for ruck straps for long periods of time, if I know I'm going to be wearing for a while I will usually choose a multi-layer back carry like Giselle's back carry (my fave) and finish it off with a tibetan tie (video here, or a double hammock/chunei back carry (video here). I can comfortably do the first carry with a size 5/4.2 meter wrap and the second is easier with a size 6/4.7 meters.