IMO: It's a matter of personal choice.
If you have a lot of work to do, then air tools are the way to go because they're lighter, smaller (easier to store), more efficient, and will last a very long time as long as you oil them & keep out moisture.
The down side of air tools is that you will need a minimum 5HP. compressor, dryers (particulate & coalescing), pipe/hose/fittings, air tool oil, and 220 volts in your garage.
A larger cash outlay, but pays off if you use your air tools to make money. Obviously, your air hose length dictates where you work.
Corded tools are cheaper for the overall outlay of cash, only require 110 volts, easier to use wherever your needs are. However, they can overheat and burn out sooner than their air counterparts. There is also electrical safety concern with corded tools. However, most modern ones are double insulated or well grounded. So there is little risk, unless you're standing in water.
My vote: If I was starting out, and just needed something for my own use, I'd go corded. However, I'm set up for air, and do enough side jobs to justify the compressor investment.
Good luck.