The installation guide for the ADC-VDB770 can be found here:
Is it just a matter of removing the old one and connecting the existing wires or do I need to change out the transformer?
Is the current camera just using a standard doorbell transformer or is it a custom transformer for it? The VDB770 uses a standard doorbell transformer.
The VDB770 power requirement for the doorbell transformer:
AC transformer with a power rating of 16-30V AC, 10-30VA.
Would I be able to use the existing mounting holes (ie are these pretty standard?) or would I need to drill new ones?
An image of the back plate and screw holes is found in the guide linked above. It’s likely the mounting is not identical.