I'm not familiar with Hong Meiling, so, I'll have to go by the profiles:
Well, Hong Meiling isn't as strong as Garnet, going by what people are saying, the difference isn't that huge, but still, Garnet still has an advantage. Hong Meiling is also over twice as fast, but OP stated that speed would be equalized if needed, so, this solves that. As for who is a better fighter, I don't know, Hong Meiling's article mentions that she's an expert martial arts, but Garnet has thousands of years of fighting experience so, I can't tell.
As for hax, well, they both have Superhuman Physical Characteristics, but Garnet is slightly stronger, so, she has an advantage on that. Garnet also has better Regenerationn (Hong Meiling can come back from decaptation, while Garnet can come back from a small piece of her body), and Garnet has Type 3 Immortality, so, that's another advantage she has. Garnet also has some abilities that wouldn't be useful here, like defusing, creating bubbles or adapting to gravity, those wouldn't really help her, so, they don't matter. Hong Meiling can fly, something that Garnet can't do, so, she has an advantage on that, same thing with Qi Manipulation. And Hong Meiling also seems to be far spperior in a distance fight, Garnet has some projectiles, such as her Rocket Gauntlets and eletricity, but Hong Meiling has Danmaku, so, she could just fill the battlefield with projectiles. Garnet also has Electrokinesis, which would be useful in a close fight, but wouldn't do much against a Danmaku user in a distance fight. Garnet has Precognition, which would help an awnful lot, so that's another advantage for her, and her Pain Tolerance could also help in a close fight.
So, yeah, Garnet seems to win this if it is a close fight, but Hong Meiling has an advantague in a distance fight with her Danmaku, Garnet does have Precognition, which could help her do dodge it, but I don't know if it would be enough to deal with Danmaku, and I don't know if Hong Meiling has any way of destroying Garnet with that Regenerationn, unless she manages to puff her and destroy her gems.
Overal: If it's a close fight, Garnet wins, she is stronger and is at least as good fighting, and her Precognition, Regenerationn, Eletricity and Pain Tolerance would give her even more of an advantage, Hong Meiling wins in a distant fight with her Danmaku.