Depends (not those) on the product. I found that things like tools, electronics, guns, automotive parts, home appliances, outdoor equipment are usually better quality from the big names. Sometimes much better. Same with most food. Occasionally I find a generic or off brand that is comparable with the big names, but not that often so I tend to stick with the brand names. Especially true with most (not all) brand name vs generic prescription meds in my experience. However, I don't feel that applies to as many of the OTC meds.
One notable exception with something I buy a lot of is gasoline. I can't tell much diffidence between brands. Same mileage, same performance, etc. I do buy from a big name supplier but that's because I get a nice lifetime discount due to past employment.
I guess I feel the old adage is pretty good, you get what you pay for. Most of the time.