Likely case would be Hitoshi wins, I would say.
Lelouch has technology that Shinsou doesn't, yes, but at the same time, Shinsou's Brainwashing is much more powerful. Lelouch's Geass (at least, from what is stated on Code Geass' wiki page statement) doesn't prevent people from doing anything outside of the command, as long as it doesn't distract from the task given. Whereas, upon use, Hitoshi's quirk paralyzes the opponent until given a command, and they'll carry out the command linearly and only that command.
Additionally, while Hitoshi's intellect isn't that high (higher than average, yes, but definitely not infinite), he was shown to be incredibly charismatic, to the point that he caused Midoriya, who knew how his quirk worked from Ojiro's advice, to still fall into his trap.
As such, while Lelouch has the physical power over Shinsou, Shinsou's general charisma and Lelouch's arrogant and volatile mannerisms would lead him into Shinsou's Brainwashing, which has only been shown to be resisted by Izuku, and that is for a completely unknown reason (I'd likely acquit it to the combined consciousness of the previous OFA owners, but there's no real way of knowing). As such, the only way for Lelouch to win is for someone to hit him hard enough to knock him out of the brainwash, which, in a 1v1, is impossible.
So, despite Lelouch's intense firepower, his arrogant and volatile personality would make him too perfect of a target for Shinsou, and Shinsou is charismatic enough to lure him into a trap with ease.