A motor oil is a motor oil. They all have the same chemistry. Mixing and matching different brand has no effect on lubrication efficacy. Shell oil won't suddenly separate if in a mixture with Chevron oil.
The key difference is the additive package that each manufacturer claims is better than the rest. This too is far fetched because there are no proprietary wonder molecules that are exclusive to a manufacturer. There are only a handful of compounds out there that will do detergent duty, serve as viscosity index improvers, etc. For example, do you think a liquid form of titanium is going to make an oil better? Or does it sound like it would make an oil better?
For example, it's like a drug. There is a type of drug, and there are brand names of it. For example, ibuprofen. There is Advil and there is Motrin. Same effect, different names.
Everyone has their preference. However, thankfully, an engine is not a human body so we can be a bit more flexible with it. It won't notice the difference if the name on the bottle was Castrol/Pennzoil/Mobil/Amsoil/Shell/Chevron/Valvoline. As long as it is of the correct viscosity, with the correct amount of additives, the engine will continue to go along smoothly and quietly.
Nowadays, conventional oils are getting quite comparable to synthetics. There are even conventional oils whose majority of base stocks are "Group III" variety...which is also the same base stock used in synthetic oils marketed as synthetics.
What this means is that...they come from the same family of molecules. Until we get into the world of esters, which are totally different in structure to an alkane, your engine won't notice the difference.
As long as the oil is API certified, it should be fine in the engine. Synthetic or conventional...doesn't matter. Synthetics are mainly marketed now for their longer drain intervals, due to their manipulation in the lab that allows for the molecules to be identical to each other. Also, manufacturers inflate them with more additives and market them as such. Sort of like a 911 and a Cayman. The Cayman will always be faster around the track. If it was given the same engine as in the 911 series, it would cannibalize the sales of the 911. So...the manufacturer handicaps it.