I've leased both for the past three months. My impressions are as follows:
1) I hate the Volt bucket seats. They are hard and uncomfortable and you sit down real low. My solution was to fold up a blanket and put it on the seat. A world of difference. It's soft and comfy, now, and I sit up nice and high (and at 5' 11", I'm not short).
2) The Volt's ride feels "heavier" than the LEAF, most likely because the Volt is lugging around its backup generator and a few gallons of gas. Sometimes I like the feeling. Other times I like the more light and bouncy feeling of the LEAF
3) The Volt has a more classic sedan look. I find it much more attractive than the LEAF styling.
4) For driving ranges up to the usable capacity of the battery (somewhere around 40 miles), the Volt acts just the same as any electric car. Smooth and quiet with nice low-end torque. Essentially the same as a LEAF
5) For driving ranges beyond the Volt's usable battery capacity, the backup generator kicks on. If you are used to driving an electric car, the sound and vibration is noticeable, but not overly objectionable.
6) You never have to worry about the battery. If you don't have TOU rates from your utility, just plug the car in when you get home and unplug it when you are ready to leave. It will take care of itself to keep the battery cool, and unlike the LEAF, it will properly maintain the charge on the 12V battery even if you keep it plugged in indefinitely.
7) No more worry about range limitations. Once the battery charge is depleted, it will shift seamlessly and automatically to charge-sustaining mode. If you never drive beyond your battery range, it will still kick on the backup generator once every six weeks for about ten minutes to make sure it's running properly. After about a year, it will kick on the backup generator for an extended period of time to burn off your stale gasoline, so you might just as well use it during the year, or the car will still burn if off at the end of the year, whether you want it to or not.
As a general rule, the Volts have proven themselves to be very reliable. It comes with three years of OnStar support, so system diagnostic help is just a push-button away, if you ever need it. There are, also, insurance companies like State Farm, which may give you a discount on your insurance premium if you allow them to monitor your OnStar stats. For low-mileage drivers, this is a plus.