I've used both with my last baby. (disclaimer -- I sell Mobys and not Sleepys but I have used both extensively).
I love the Sleepy Wrap fabric, and the fact that the edges curl in -- I found it looked nicer than the Moby, and it was just totally cuddly. OTOH, I didn't find it as supportive as the Moby and my big heavy baby outgrew it more quickly than she did the Moby. I don't think any stretchy wrap is suitable much beyond 20 pounds, FWIW (no matter what the carrier companies say).
It's definitely not going to be any cooler than the Moby. Both are cotton jersey and are pretty warm.