word choice - Differences between 度 and 回 when counting occurrences

What are the differences between using 度 and 回 when used to count number of occurrences?

For example:

1. 
   
   

   そんなことは一度もしたことがない

   
   


2. 
   

   そんなことは一回もしたことがない

   
   

Are there any restrictions on what kind of actions referred by そんなこと that can be used with 度 or 回 in the examples above?