The only thing I feel I can add is that Shuka generally moves around a lot and never stays in one place unless forced to by the battlefield. The Colloseum gives Shuka an avenue to move around in tricky patterns and stay airborne, which she prefers. She will generally never approach her opponents and keeps enough distance for them to be in reach of her threads and wires, which she can also use to attack blindspots or areas even without line of sight.
As a recap, Shuka has faster movement, much faster reactions, more arsenal, more versatility, and better maneuverability. She excels in spacious locations with many walls/buildings/obstacles/etc.
Connor is smarter, has precog and info analysis, has guns, and is much better at melee combat.
I guess I should mention that Darwin's Game has a character with
precognition and information analysis. She and Shuka are allies, so they never fought, but Liu Xuelan was literally too fast for Rein's precog to catch her. Shuka isn't at Liu's level, but she's fought her to a standstill and is still one of the fastest characters in the series. Rein would as such likely have trouble keeping track on Shuka if she were to fight seriously.