The biggest differences between most of the bike brands available today are, in my humble opinion, the retail and service experience you get (bike shop vs. big box store, for instance), and fit/color/style differences between brands. For the most part, all bikes are using similar components in a given price range and bike frames are even made in only a few factories under contract to big brands in Taiwan and China. Because bikes are commodity items, the most important things to consider are warranty and service after the sale (if that's important to you; it may not be) and personal fit on the bike. If your a DIYer and service the bike yourself, you might get a lot of value out of a big box situation because you can do some the needed tweaks yourself.

You said you're buying used, and the biggest factor for used bikes is condition and maintenance. A new Trek can fall apart quickly if left outside under the deck. And a Schwinn can last for many, many years if cared for properly. The reverse is true also, of course.

Note that Giant, Trek, and Specialized are their own brands. Raleigh and Diamondback are both owned by Regent, LP. Cannondale is owned by Dorel, who also own GT, Mongoose, and Schwinn. It doesn't mean that Diamondbacks are the same as Raleighs, just with a different paint color, or that GTs, Cannondales, and Schwinns are all the same bike. But it demonstrates that the brand name doesn't necessarily mean as much today, when private equity companies buy and sell brand names, as it may have in the past, when each brand made their own stuff in their own factories.