I carry both a mini-pump and CO2.

The CO2 is for group rides so people aren't waiting too long for me. And for unbearably hot days when I don't want to waste energy pumping.

But 95% of the time I use the mini-pump.

My favorite mini-pumps are the Topeak RaceRocket, HP and longer HPX. Best ergonomics I've tried for mini-pumps. I also have a Blackburn Core Slim which is comparable to the Topeak RaceRocket HPX, but the ergonomics aren't quite as good. The Topeaks have soft plastic end caps and rubber grips. The Blackburn has metal end caps with squared edges, and no rubber grips. I use my gloves or a bandana to cushion my hands when using the Blackburn.

All three have short hoses and threaded chucks. The RaceRocket HPX plastic end cap doubles as a Presta valve core wrench. The Blackburn Core Slim has a metal core wrench in the end cap.

On group rides I've seen other riders blow out their only CO2 cartridge and had no backup plan. In one case the fellow's spare tube was also punctured because he missed the bit of glass or thorn that caused the first puncture. So I've let them borrow my mini-pumps. And I also always carry a patch kit, usually the Lezyne self-sticking patches, although occasionally the self-sticking patches by Park and others. Lezyne are the best but not easy to find locally.