I carry a known good tube and swap on the road, then patch at home. Patching done at home is much less likely to fail, because you can take the time to clean the tube well (whatever cornstarch or talc you lubricate your tube with will interfere with the seal if it's not washed off well, never mind any other microscopic road dust that might have gotten into your tire), and you're not tempted to apply the patch before the glue is completely dry. I carry pressure sensitive patches in my seat pack in case I have more than one flat on a single ride, but I've heard that they aren't as reliable as the old-school rubber cement kind.
Plus it's just easier to find the hole when you can dunk the tube in a pail of water, unless either the hole or whatever penetrated the tire is pretty large. Lining up the valve stem with the tire label when you install the tire will help with that, especially on the road - if you find something in your tire, you can go right to the hole in the tube, and if you find the hole in your tube, you can find whatever's stuck in your tire.

