I got mine from Bergdorf which frequently has great cashback deals.
Yea, the large is much bigger. Medium looks great crossbody, large to me does not. I feel like someone has to be quite tall to pull off wearing the large size crossbody.
When I wore the large size with the attached shoulder strap, it felt really heavy and uncomfortable. Not sure if it is heavier because croc is slightly heavier and/or if it is just due to the size. Plus, at least in the croc, the bag was also wider, so the bag sat farther from the body which also made it awkward to shoulder carry.