I carry just a minipump on most of my bikes except the one I also commute on where I carry both a minipump and a small CO2 inflator chuck and one CO2 cylinder. I've only used the CO2 twice because I prefer to just use the pump.

The advantage of CO2 is speed of inflation, disadvantage is that it's one time use. The minipump is the opposite, slower to inflate but you can use it until it breaks. Most of my minipumps take about 150 to 200 strokes to reach an acceptable riding pressure for me (around 70-90 psi in a 700x23 mm tire).

Twice on rides of only 50 and 80 miles I've seen other riders flat three times. Lucky they were riding in our group, it's a little more trouble when solo. That's why I prefer the insurance of a minipump as well as carrying a few stick on tube patches in case of more than one flat on a ride.