Both have their ups and downs. It wouldn't be practical to fill a CO2 tank with your air compressor. But if you can afford to have an air compressor
AND a CO2 tank for those trips where you want to take it, then you will have the best of both worlds.
I go into a little more commentary
here
In a nutshell, if you can only choose one or the other:
1. If you don't plan on doing an extended trip somewhere that will exhaust your CO2 supply, then you will probably enjoy the CO2 more because it is much more powerful and much faster than a compressor.
2. If you don't like the idea of running out of CO2 on an expedition somewhere, and you don't like the idea of having to refill your CO2 tank (costs time & money) then you might want to choose the air compressor.