1. No grounds or lipids at all with aeropress, due to the paper filter. Even a good french press will let some grounds into the coffee, and all of the lipids. You can remedy this by popping a paper filter under the plunger, but that's kind of hacked together.

2. You should actually be stirring coffee with a french press as well. If you don't stir with a french press you may as well not stir with an aeropress, they both brew in similar containers.

3. No fine metal parts or glass so it's ideal for hiking, don't have to worry about something shattering in the pack.

4. I prefer the volume and taste of aeropress coffee over espresso or moka pots.

Anyways I'm not saying there's a perfect solution or a right way to prepare coffee. These are just the reasons I like aeropress, even if I do make a lot of french press as well.