quetzalcoatl or francis drake

Drake for speed farming

Both are great
Drake are top-class for generally farming, no matter daily quest, or mob cleaning. She has excellent self-sufficiency (NP/3rd skill <--> star <--> Np gain from critical art card/2nd skill). But she cannot be very good for fighting boss compared with Ozy/Quetzalcoatl, except you have her in team with Waver/Merlin

Quetzalcoatl on the other hand is excellent for boss-killing. Although she also required good support, but even Hans/Shakespeare can be her support to kill a enemy boss. What you have to do is just prepare a good turn for enough star to trigger her critical NP-x-B brave chain.

Both good. Also you can build Rider critical team if you have turn-based star generation CE. In this case, even Drake can slash caster boss in few turns, since riders are natural for critical damage but she is quite good for self sufficiency then make good cycle of her damage.

I would pick drake first because we need farmers more often than boss killers. Also note that if you are really just a few hours into the game, the material you need to ascend quetz is locked behind clearing Babylonia unless an event has some in the shop.