My mother would dust her rising dough with flour and cover it with a dish cloth, today everyone uses oil. Which works better? What's the difference?
In both cases, the goal is to keep the dough flexible so it can expand as it proofs.
With flour dusting, the proofing dough is usually stored under a damp towel, so that the moisture keeps it from crusting over. The flour is really to keep it from sticking to one's hands or the counter, and therefore easy to handle. Proofing periods also tended to be shorter--a few hours at most--so even a dry towel would often be good enough.
Oiling the poofing dough makes a moisture proof barrier, so it cannot dry out and therefore crust over. With the rise in popularity of high hydration breads (lots of liquid in the dough), the soft dough is hard to coat with flour as it tends to get absorbed; oil is easier to apply. It also is suitable for longer proofs like overnight fermentation that are more and more popular. If course, it does introduce a very small amount of oil into the loaves, as well.
I would hesitate to say one method is strictly better than the other, but rather that each are effective in their context. If I was forced to choose, I think the oil method is more flexible to more types of loaves, but may be somewhat messier.
I've experimented with both methods for pizza and bagel dough. They both work fine, but (in my personal experience only) I find using oil works better if the dough is allowed to stand for more than a day. If used within the day there is no difference.
I also happen to like the added flavor of olive oil (which I use exclusively for doughs) so I favor that.