Too vague a question. Why bitless - any physical issues? You don't need an excuse but if the horse is backed with a bit - why are you looking to change? How have you transitioned? What background does the horse have? What are you planning to do?
And no - a side pull does not mimic the action of a dually....
I agree that a bit more details would help us answer to your question better.
I myself have been using an Orbitless for years now. My horse shows strong preference for it over any other bitless bridle we've tried, and I love the versatility of options it gives, going from a simple sidepull to a light hackamore with just a change in the rein position.
I have heard nothing but good about the Transcend Bitless Bridle. It comes in a nice range too. look on FB, you can discuss it merits with the designer and other users.