thank you for your question (and your answer).
I used Profile Builder myself on a couple of sites and the compatibility issue between it and EZ Emails is a little harder to fix.
As you have already noticed, PB defines its own message template.
If it were only that, it would be easy to give EZ Emails priority in defining the default message.
But that works only when an administrator create a new user.
If you, as an administrator, create a new user both you and the user receive the email with the template defined in EZ Emails.
The problem is that Profile Builder completely redesigns the registration form, allowing you to put it in the front end with a shortcode. When the user signs up using that form, the WordPress notification system is completely bypassed and a totally different function is used in its stead.
I will try to find a solution to filter that as well.