I used to have an article from I believe consumer reports or Popular mechanics, honestly can't recall. Anyways, they had tested a whole bunch of NY city taxi cabs using several different mineral oils and several synthetics plus a couple using additives such as "slick 50" which was a silicone additive and quite a big deal back then ( I believe the article was from the 90's). Anyways, they changed the oil every 6,000 miles...yes, 6,000 miles on a taxi that sat in traffic going nowhere half its life. Then at 200,000 miles they tore them all down and measured wear. Guess what? There was no significant difference in wear between any of them. Based on this, I changed the oil on my 2003 Saturn Vue whenever the computer told me it was required which averaged a little over 10,000 miles. At 240,000 miles I traded it in and it consumed about 1/2 quart in 10,000 miles which is pretty respectable. The oil never smelled oxidized. If your oil has that horrible smell to it, it has oxidized and that is bad as it will act as a catalyst to oxidize the replacement oil quicker and if that happens your going to be forced to change it more frequently.
What is the biggest performance difference between synthetic and mineral oil? Two things and they both have to do with temperature. Synthetics will maintain a better viscosity index, meaning viscosity will change less over temperature. Translated that means they will flow better in extreme cold and not thin out as much in extreme heat. The second is that at extreme heat, they will not break down as quickly and oxidize or evaporate. This makes synthetics much better for heavy duty use in extreme heat (like pulling a 5th wheel through the desert for example). What others have said about synthetics leaking more is also true. If it were me, I would use a 10w-40 with zinc or add zinc if it doesn't have it. The zinc replaces lead which is no longer put in gasoline. The zinc is a lubricant for the valves on older cars designed for leaded gas. With a modern rebuilt engine it is usually not required but you will need to confirm this with the engine rebuilder.