You are right to taste a difference! As Jennifer S says, time plays a big role in how the end result tastes. However, there are other factors: temperature (hotter = more bitter), pressure (time, temperature and pressure are all required in some combination, so for a particular technique, increasing the pressure can mean that the working temperature and/or time can be decreased), amount of coffee (Aeropress generally takes a lot more ground coffee compared to a French press, but you will get a much richer flavour IMO), and coarseness of grind.
You can vary all of the above for any method, but different methods will be better suited to different 'values' of these, or at least will give different results.
Finally, there's filtering, and how the grounds are removed from the end product. A French press will leave more sediment in the coffee than an Aeropress/drip, as the metal filter will let more grounds through than paper.
My advice would be to trust your taste, but also think about practicality. I like the taste of Aeropress best, so I use that if making 1-3 cups, and it's great for travelling. If making more, I'll probably use a French press, or if I want to make a lot of 'espresso', I have a huge moka pot.