I tried both, and for the coffee I use regularly (which isn't as good as it could be, it's not high grade, and it's not fresh ground - it's also less than half the price of "proper" beans) -- I can't really tell the difference.
For really good coffee I haven't tested back-to-back, but I generally find that letting it steep "right way up" is fine. Also letting the coffee steep in a pre-heated cup/kettle/teapot is fine. Maybe this makes a difference if one makes "pretend-espresso" rather than a full cup of "Americano" (actually more like Lungo -- but still not, as the pressure is lower than the initial pressure for a lungo).
I like my aeropress, but it's no espresso machine. It's different from a French press and a pour-over -- but I'm not prepared to claim that it's the best coffee.