Agree with others that impact drivers will be more powerful than an air ratchet, but due to the size of them they aren't really comparable tools. If you can fit an impact driver then you can fit at least a M12 Stubby Impact that will hit harder than an impact driver. The other issue is even if the driver tool itself is somewhat smaller, most have 1/4" female hex chucks, so you'll need an adapter to use sockets, which makes the tool way too long to fit into any tight spaces.
I've started warming up more to my M12 ratchet, but it is quite low on power. Still useful for under the hood type stuff, smaller bolts, stuff with clearance issues, etc. I pulled a splash shield from under my wife's SUV while it was on jack stands in the driveway, so limited clearance. 12+ small bolts, and the M12 ratchet made fast work of it.
Milwaukee also has a newer M12 right angle impact that might be the closest thing to a "best of both worlds" tool that you're looking for. But even with that don't expect huge power, I believe they test out with lower power output than the M12 stubby impacts. It will be a solid jump in power from a cordless ratchet though, won't snap your wrist, and has quite good clearance.
Really it's not ideal to hear if you're trying to save money, but there are situations for each of these tools. And situations where only that tool will work, and the others won't.