Gao is better in everything except for dps. His Range makes him useful for a lot of units that outrange Gaia. Survivability does matter, and it's a huge advantage to Gao here. Multihit lowers her practical dps so it isn't as absurd as it appears on paper. Gao has the definite advantage for waves, whites, and metals. Gaias ld is neutral for her, I'd say it's bad because of the huge blindspot and only 200 width, but it helps multihit not miss quite as much.
All Gaia has on him is dps, it's a big difference, but Gao wins everywhere else unless you care about 1k price lol.
Price hardly matters for long cooldown units like ubers, its important for meatshields and decently so for midrangers, but for ubers it doesn't affect much.
Ama is in a similar situation to Gaia against Gao, except she only has 200 more dps, which isn't much of anything. He destroys her survivability wise, has more range, less tba and animation. Add on top of that being better for waves, metals, and whites and its pretty clear that Gao is better.
If you think 1k price is more important than all that, give me reasoning please.