OK. The most notable difference between the DRV8834 and DRV8825 is the input voltage range. The DRV8825 would not work with the 5V rail on your supply and the DRV8834 would not work with the 12V rail. The maximum speed you can get from the motors with a 5V supply will be lower than it would with a 12V supply. There is an issue with distorted microstepping using the DRV8825 on some motors and the specifications for your motor are close to where we have observed those issues, so we cannot tell whether or not it would be affected.
If you need precise movement but not high speed operation then using the DRV8834 (with the 5V rail on your power supply) would be a good option. If you care more about speed, then the DRV8825 with the 12V rail is a better option. Also, our TB67S249FTG Stepper Motor Driver Carrier supports 1/32 microstepping, will work with a 12V supply, and should provide accurate microstepping with a motor like yours.