I think that "it rides great" is a common response to riding a new-er (to us) bike. But if you'd compare its ride to one of your finer bikes over a stressing course, where you must shift, turn, climb, accelerate and flat out burn, you'd find that it's not that great of a riding bike. That's where the dividing line is. Good enough is the enemy of better, in this example. Sell the Schwinn...be done with it.
I'm adopting the attitude that all [of my] bikes must work for their living. If I don't ride it and use it regularly for some purpose, it gets sold. I hand my wife the cash for deposit in the bank. She likes receiving the money. I like removing the clutter. The buyer likes buying a bike that's in perfect mechanical condition (for whatever it was designed to be).
Does this help?