I'd say he gets to either Gordon or Samus, they are kind of even with him, it'd be one hell of a fight though.
I don't think neither of them are actually immune to mind control, however, it is resistable though very hard. It is totally unknown what would happen if he tried, so I'm going to assume that they can repell it.....
Gordon does have an insta-kill with his upgraded gravity gun, so in that way he would win. However, he has nothing to see invisible people with, and Psycho Mantis can make himself invisible. So if he does that, he wins. He can also teleport and read his mind, he'd easily dodge almost every shot before fired....
Samus has one hell of a suit. No matter what, I doubt Mantis would have any way of getting through that tough shit. And since I've ignored the mind controll thing I he doesn't have most of his potential at use. However, he could spare some seconds by turning invisible, and teleporting around the room.
Also, a friend told me that Samus visor is controlled by a camera, or a power source of some sort, so that if someone jacked into her suit, her view would be disrupted. If this is true, Mantis could easily jack into that. Also, he can read her mind, so he will know when she is to fire her weapon, also, if she fires missiles or explosives or anything like that, he can destroy it instantly when it is fired (yup, he did that in MGS 1), meaning that it will only hurt Samus.
He can also make people temporarily blind, and take over their view, making them see through HIS eyes, making it damn hard for them to control their real body.
Samus would be one tough shit to get through. Unless he can slap her around in her suit or disable it somehow, I doubt he would win...