What's the difference (if any) between these two types of PEX-to-copper fittings?
It certain makes a difference - apparently 70 cents.

Functionally, no difference, or possibly (hard to be sure from the small images and I'm not going to bother to hunt down the parts elsewhere) the brass is set up / sized to be a  male part for soldering into a female copper port, while the copper appears to be a female copper port to have a male copper pipe soldered into. The machined exterior on the brass part leans that way, but could simply be the way it's made. i.e. depending on what size the part is, it appears that it could be either. 

Edit to add: the brass might also be slightly shorter, but that seems unlikely to matter 99.9% of the time.