In my experience, it's up to you to present the classification and rationale (MDD rule) for your device, and NBs will review and either agree or not.
...so if your NB agrees with your rationale for Class IIa, then great!
The fact that a competing (equivalent) device has a different classification through a different NB probably just means that the other manufacturer or NB has adopted a different interpretation of the rules with respect to their device.
Because (I presume) you and your competitor's devices are not completely identical, this may be a result of, for example, different materials, differently worded intended use/indications, or perhaps simply a more conservative definition of "potentially hazardous" when assessing the MDD rules.