I own both. The 870 fits me better, but I can shoot both equally. I am left handed, and used to have trouble with the 870 safety, until I had my gunsmith reverse it. $60 later, I had a right handed 870 with a left handed safety. Also Remington make an LH 870, It just costs more, above the cost of the RH model, than converting the safety. The palm swell on the mossberg is my only gripe. I have a new stock on order. It sucks being left handed and short!
Get either one. They will both last a long time if you take care of them.
IN my case;870-13 years and counting
500 20 years and counting. See which one fits you best and go from there.