I couldn't vote, because I do both. I buy a lot of generic things. For general purposes, flour is flour, sugar is sugar, etc. There are certain store brands that are very good...for instance, I have never been disappointed in Kroger Brand or Best Choice items. It really all depends on what you are cooking.
If you're making tuna casserole, a can of Best Choice Peas will fill the bill. If you want peas to go with your steak and baked potatoes, you need Le Seur.
Some generic things are worth a try, even if you're not sure. For a while, one of our local markets had a "bargain" aisle. I bought some Polar brand crab claw meat there, for $1 a can, that was delicious. I tried some generic spaghetti sauce from the same aisle, thinking I could season it up, and ended up throwing it away the minute I tasted it. (Nasty!)
In regard to non-food items, once again, it depends on what I'm buying. Generic toilet tissue and paper towels are no bargain. Give me Charmin Ultra and Bounty all the way. The cheap aluminum foil isn't any good either.
But I always buy generic aspirin, acetaminiphen (Tylenol), and other medications all the time. You wouldn't believe how much cheaper the generic "Clariton D" is than the original product.
Unlike foods, you can actually look at the packages on these things and compare the ingredients.