If you mean comparing Mopar brand conventional motor oil to Walmart Supertech conventional of the same weight and certifications, I'd think the difference, if any, is probably so small it wouldn't matter over the time between oil changes. JMO
In the final analysis, no manufacturer is going to put their best quality in a private label unless the label is paying for it in which case it will cost the same on the shelf. If they want the identical product at a bargain price, they'll get laughed at; the manufacturers would be underselling themselves.
The differences are in the base oil and additive package used. There are MANY different ways to end up with a final product that will give VERY similar results. For "most" people, following the vehicle mfg. recommendations regarding grade and change interval using any API certified oil will result in an engine that outlasts the rest of the car.