Thank you everybody for the awesome replies. They really helped me to understand the strengths and weaknesses of each bike.

The Diamondback is out of commission for the next weak, while a new rear wheel arrives to my LBS. I am going to look into changing one or two of the chainrings, and maybe swap out the gripshifters for normal shifters. Some new brake pads are also needed for the cantilever brakes.

So I spent the weekend working on the Schwinn, just to make it road worthy, and transferred over a bunch of accessories from the Diamondback. The tires, rack, fenders, lights and pump moved over, and I installed some new Power grips onto the pedals. The gripshift for the front was toast, so I now have an old Shimano shifter for the front, and a gripshift for the rear. Kind of odd, but i don't want to put any real amount of money into it. I did buy some cheapo bottle cages for it this evening. I'll road test the Schwinn on Tuesday, with a 15-mile ride out to local park, hauling my daughter in her trailer. If the bike falls apart, the wife will be available for a quick pickup. If the ride goes well, it will get commuter duty for Wednesday and Friday.