Hm, I've never used a mei tai, so I can't really speak to that much. I own both a gauze wrap & RS & LOOOVE them both. Here is my rundown of pros & cons:
Wrap - pros:
more comfy (weight distributed all across the fabric, on both shoulders instead of one)
Since it's more comfy, better for heavier kids. (I stopped using an RS regularly when DS was around 12 mos)
more versatile (can do front, back, lots of diff carries)
While it's close, I would say the gauze wrap is actually the cooler of the 2. Although you could get an RS made with gauze fabric (or have one made).
You do still have all the fabric wrapped around you, but it's amazing how light & breathable it is. I bought a Wrapsohdy bali breeze & even in the crazy heat of Baltimore July when my DS was born, I didn't feel any hotter than I would have just carrying him.
RS - pros:
Shorter learning curve - much easier (back-wrap cross carry took me FOREVER to master)
Much quicker to get baby in & out (by contrast, I stopped doing back-carry with a wrap by maybe 13 mos because it was too much time to get him in & out & since he was walking, he wasn't content to stay there for long periods)
I always did hip-carry in an RS. I agree it is likely to bother your back to do a front-carry with a heavier child. With hip carry, some of baby's weight actually rested on my hip, so it wasn't all on my shoulder, so that helps a lot. Also nice that he can look forward more easily than a traditional 'front' carry.
If you can swing it, I totally recommend both. You can get a decent RS used - I like Maya Lightly Padded (I do NOT recommend Maya old-style sewn-shut shoulder!) I got mine barely used at all for $40.

& you may notice I stopped using both of these things by about 13 mos. Now I use an Ergo. LOVE how it transfers the weight to my hips in a back carry. I've worn him an hour easily when hiking.
Another plus is that DH will wear it. I got him to try wearing DS in the wrap once, but I did it for him. I don't know that he has the patience to master wrapping or even an RS - plus they both just seem more feminine, so I think he's more comfortable in an SSC (seems a common thing.)
But I love babywearing, am PG now with #2 so I'll get use out of everything, and I know all these things retain some value so I can resell them & get some money back. So I don't feel bad having this nice stash.
If you need to buy just one, I definitely recommend trying them out - trying to walk around in them a little while, put baby in/out repeatedly to get a feel. There are so many pros & cons, it's just such an individual thing.
Follow Mothering