The purported "benefits" of Damon braces include shorter treatment time, less pain and eliminating the need for extractions.
Dentists may like Damon brackets because it is less time-consuming to change wires.
The purported benefits are mostly marketing claims that have no real impact on the biomechanics of how teeth move and how an orthodontic case is planned. Your teeth ultimately cannot sense if you are wearing regular brackets or Damon brackets!
The UK Advertising Standards Authority passed a ruling on claims by Damon (Ormco) which you can read here. More information regarding self-ligating braces claims can be found here.
If you can afford the additional premium for Damon brackets, then they will do no harm. I would, however, encourage you to be more cautious when evaluating claims about the efficiency of different bracket systems. Asking your provider to show you examples of cases they have treated that are similar to yours would be more helpful than fixating on the brand of brackets used.
Ultimately, it is the clinician that makes the greatest difference in the results obtained over the choice of bracket system.
