hook_entity_base_field_info() vs. creating a new entity I need to create a fairly extensive user/account management section of a site.

I'm wondering whether to just extend the existing user entity, or whether I should create a completely new entity to house all the extra stuff I need...

Are there any pro's/con's I should bear in mind when making this decision?
There isn't a 'right' or 'wrong' method of this. It really depends on your business requirements.

Are the fields you are thinking you need related to the user object? If they are, then I would use the User object. However, that shouldn't involve extending it, you can just add fields to it.

Without more information it's hard to be more specific.