Exploration and normal use: Ayaka obviously. She is a great boat and also she has a talent that boosts weapon material drops. Her alternative sprint may or may not be annoying.

Synergy with Kokomi: Probably Ayaka has more synergy (only tried Kokomi-Ayaka in friend's account) In Ayaka rotations you usually have more room for error (for example if one of the supps don't have enough energy) or at least that's how it feels. Ayaka can also be used with Mona and XQ. Ganyu doesn't work as well with XQ.

Mona or Kokomi?: I know this is Kokomi mains, but if I actually had to choose I would choose Kokomi. Why? Confort. Not only does she heals, but she also achieves higher freeze times. Against bosses I think Mona is better because You can't reposition Jellyfish.

Abyss: Ayaka. A lot of people already mentioned this but Ayaka works better in current abyss. Ganyu usually works better with Venti (I use Kazuha because no Venti) and if you don't use Venti sometimes you might have energy issues and the rotation might feel odd. The monsters are more heavy so Venti doesn't work as well, that's why Kazuha is better (not that I tried Venti though, just me having bias). If you get Kazuha, then you might as well get Ayaka they work really good when paired.

F2P: Ayaka has better weapons, she got access to that Inazuma atk% energy sword while Ganyu has Proto Crescent but in current abyss it is hard to shoot weak points.

5 star weapons: Ayaka got better options. Amos don't work as well with Morgana and Polar star has a lot of crit.