I had a nice long response typed out but my browser crashed, so here are the highlights.

The flying part is easy, its all the little things that come with flying around the world and there are ALOT of little things.
The commuters and the majors make it easy as things are pretty much canned and alot of hand holding is done or things are done in the background and you just flat out never see the process.
In the supplementals, there is no hand holding and you are basically on your own. That can be good and bad at the same time.
You go to places you've never been, much less heard of and are expected (by ops) to know exactly where to go and what to do and do it in pigeon English and and don't screw up in the process.
I have seen Capts from the majors come to the Supps and get their rear-end handed to them because of the philosophy difference in operations.

In short, flying the Supps is a completely different world.