Asterix is an adventurer, not a superhero. He doesn't go around righting wrongs, he has adventures.

Asterix isn't a superhero - he's just a normal guy till he has his potion. I guess you could argue Obelix is, since it had a permanent effect on him. Neither of them dress up (any more that the rest of the characters).

Batman is just a normal guy with a lot of money, and still considered a superhero.

The money only affects his capabilities. Rorschach only had a mask and an unshakable sense of purpose.

But Batman has a cape. Asterix and Obelix got their clothes made by Edna Mode: "no capes!".