While I don't mind the Aeropress I have a much better experience with a good old French press - much less chance of mess (stands well, no need to stir with the paddle/a spoon, no risk of putting too much pressure and something falls over).
Tastewise I've tried it with both metal and paper filters and regular and reverse method, as well as different types and grains of coffee - there's no tangible difference to a decent French press. And of course both are far far far away from a proper espresso as you'd expect in a proper Italian or Portuguese café.
The only upside I see is that it's light, so if you do carry something else to boil water it might be a good choice for campaign - but a small french press also is not heavy either. And of course if you go camping with a group a good mocha express to put on the fire makes you the hero of any journey (at the cost of an extra kg).