The main difference is in the degree of stretch. More stretchy is easier to use for a tiny, but they grow out of it quicker. Less stretchy is a very slightly increased learning curve. I would go for less stretchy if doing it all again.
Don't know how the Hug a Bub falls on the stretchy spectrum, suspect it is quite stretchy. Moby is very stretchy.
Less stretchy are GypsyMama Bali Baby Stretch or the MAM Eco.
No stretchcy si going to be very cool in summer. If feeling brave you could go straight to the woven style and get a GypsyMama Bali Baby Breeze - which are gorgeous, but harder to learn with a newborn.
If you feel the heat you may want to switch to a mei tai, but by the time summer comes you'll have more experience of what you want.
If you buy secondhand you can sell on for about what you paid and therefore chop and change till you get things right. It is quite hard to find stretchy wraps on the second hand market though as they tend to get beaten up.
You can make a cheap stretchy wrap with about 5m of stretchy cotton jersey. Cut it down the middle, voila two wraps. You can experiment with tapered ends etc should you so desire. Use the tying instructions for Moby or any other stretchy wrap - easily found online.
There, everything pretty much I know about stretchy wraps. They're fab, used a Kari-Me (very stretchy) for the first 8 months or so but DS wasn't a heavy baby. Average babies would probs last about 6 months.