BU0836A disadvantage = (Relatively) High cost, little customization - can disable unused axes.
BU0836A advantage = Ready to use, just "plug and play"
High (relative to Arduino) axes resolution (12 bits - 4096 points)
Arduino disadvantage = Not ready to use, need flash firmware (theoretically an 5 minutes job), choose parameters. Low (relative to BU0836A) axes resolution (10 bits - 1024 points), can be increased for 14 bits with external ADC (MPC3202/8).
Arduino advantage = Low cost, customization with available ready to use code (e.g. MMjoy2, EJoy32) or user developed code (require code knowledge).
Firmware support TLE 5010 "magneto resistance" sensor, in digital mode.
I have used both in the past, both do the job well, just mater of preference, convenience.
But since you already have an BU0836, use then.