I can't remember AutoZone or Advance Auto. But NAPA oil is made by Ashland who also makes the oil for Valvoline. Some people claim they are the exact same oil, just in different bottles, however some people have said that Valovline claims them to be the same except for a slightly weaker additive package in the NAPA oil.
Quite a few people stocked up on NAPA synthetic b/c it was on sale for $3.29 a quart (sale ends today), so I expect we'll be seeing some new UOA on it soon enough.
There are differences between house brands and a predominant name brand like Pennzoil conventional. YB is generally understood to have a great base oil and a solid additive package. But at this point you'll be hard pressed to find a SM/GF-4 oil that can't do 4k mile OCI with normal real-world usage.
If you're looking to save a few bucks on your oil changes, at my local Advance Auto the Formula Shell is cheaper per quart then their house brand. It's actually the cheapest oil they sell, and I'd personally have no problem with using Formula Shell in my car for 4k miles (though my driving conditions may differ from yours). Also, if I shopped at Walmart, it'd be hard to pass up the 5 quart jugs of Mobil Clean 5000 or Motorcraft. Both have shown solid UOA results and both are priced very competitively