Not sure polling rate would help.
Increasing it would allow you to change directions slightly faster, but the movement in any single direction is an analogue speed value.
The reason a mouse feels faster is not because of speed, rather it's the precision translation of movement, leading to ease of maneuver, which roughly feels like you've accomplished the movement faster.
The cursor controlled by joystick is not as precise or as predictable , therefore leading to a cumbersome feel, and more time taken to complete a comparable maneuver
It's mouse /keyboard vs game controller.. you can increase the polling rate of the controller all you like, you'll never beat the guy with the mouse.