I usually only use the USB cable. Remember that it takes a good bit of drain to actually cause it to turn off, so even half a battery will get you through most workouts.
If this is a frequent occurrence they do make one-use battery packs for cell phones that will charge the garmin. I remember when it first came out a lot of people were talking about how it was really not sufficient for anything much longer than a century, but that they had good luck by adding those chargers. I wouldn't waste it on a training ride, but if you need the extra juice it's something to consider.

I would think that they would both charge at the same rate, but if one was going to do it faster than the other, I would think it would be the wall charger.