Are the outputs the same using standard cubic foot per minute measurement?
Single stage has a much higher output temperature then two stage. If the CFM is measured at the higher temperature, the single stage is less efficient.
Due to the higher temperature, the single stage will be more stressed in operation, parts and oil
I agree with the higher outlet temp comment (more below) but I was under the impression CFM was measured at the pump inlet. However, if measured at the outlet again I could see the issue.
OP, in theory a two stage isn't more efficient but to make that theory true would be difficult. To step back a moment, when you compress air you raise the temp and pressure at the same time.
So in one case your outlet air temp is say 200F and another case say 250F, both at 150psi. Which pump is delivering more air into the tank? Well if you let that air cool to room temp you will find the 200F outlet temp air cools to 121 psi while the 250 outlet air cools to 111 psi. (PV=nRT based calculations, BIG assumption that the outlet temp air and tank temp air are the same)
So the pump that discharges the hotter air actually discharges less room temp air even though the pressure and volume of hot outlet air is the same.
So why is two stage better? Well it's better because you can install an inner cooler which helps pull heat out of the air before you compress it a second time. Is it better than an after cooler? Not sure. Both cool the air (and thus drop the pressure) before the air gets to the pressure switch. However, I suspect that a two stage system should generally have better cooling in most cases so your outlet air temps will be lower.
How much this matters for a garage user? Probably not much (not sure about moister in painting) but like many power tool choices we are often motivated by technical differences that might not actually matter in our application.