Everyone tends to focus on the lubrication properties of oil in these discussions but from what I can tell, most oils provide very similar lubrication. If all you're worried about is lubrication, it doesn't really matter much what you pick.
There are some other issues that should probably be considered, and the two main ones are corrosion protection and toxicity.
We typically expect our oil to provide corrosion protection and depending on the additives, the level of corrosion protection can vary widely. Premium gun oils tend to offer pretty good corrosion protection. General purpose oils and motor oils often score very poorly in this category.
For a carry gun, it makes sense to pick an oil that isn't especially hostile to skin contact and that's not generally a design criterion for general purpose oils and certainly not for automotive products. If you're going to carry a gun in a manner that would allow it to be in prolonged contact with your clothing or skin, it makes sense to think about potential health repercussions.