Atkin did use the Beesley type action but modified it slightly to make it easier to close. Some think the Atkin variation is superior.
In answer to the question, you would probably achieve similar money for the guns if you held out. You may see a drop in the price of 10% on the Atkin in relation to the Purdey.
Unfortunately, the name recognition factor carries a bit of a premium.
The Purdey would sell faster because more people recognise the name. The Atkin would find a discerning buyer because if its quality.