Mulan has military training.

Mulan took out an entire sentient army with an avalanche.

Merida makes a good marksman, but she does tend to make 'fatal mistakes.'

She doesn't have much experience with hand-to-hand combat and is known for her marksmanship. While that's a notable skill, it does have to be effective from a distance, putting her at a disadvantage if one happens to sneak up on her and/or she can't get the shot off in time. Merida would be best used as a team member than a solo act in a zombie apocalypse.

Mulan, however, is known to have hand-to-hand experience with her military training as well as being shown to have remarkable marksmanship skills in her own right. All around a good fighter and that would give her a decent advantage over Merida.

mulan is a better fighter

Merida is trained to fight with a bow and a sword. However, I think what would do her in is her impetuousness. She doesn't really think her actions through and can be impatient. Which is unfortunate, because during a zombie apocalypse you need your wits about you.

I think so.

This was hard but Merida sometimes fails.

What people said above.

Mulan is more quick-thinking, imo.