The big advantage is that running barefoot or with minimal shoes forces you to run with a foot strike instead of a heel strike. When running with a forefoot strike you use your calves and achilles to absorb the impact, instead of your knees, which was a big help for me. I would always get pain in my knee when running more then 10k, but that is no longer the case. I can recommend it to everyone who is into running, at least try it a bit, you don't have to run barefoot all the time, but it is really good training.
It takes some time to adjust though, in the beginning my calves and achilles would get really sore after a short run, but after about 6 months of gradually increasing the milage I can run for hours without issues.
Before switching to minimal shoes I ran on zero drop shoes (Altra) for a few months, which I think eased the transition to minimal shoes.
I'd previously been running a lot in "traditional" running shoes with a chunky soles and "supportive" uppers until several years ago when I switched to the like of the nike free range (no association, just a customer) and have never looked back. My persistent arch pain and shin splints stopped and never came back, and I don't ache the next day any more.
My advice would be to listen to your body and try some different options.