Purdey SO's have many admirers and many more happy customers but if I had to choose, I would take the H&H design every time. Why? Because having worked on both, I would be reasonably happy to repair or make any part for a H&H but would blanch at the prospect of making many Purdey parts. To take the main spring as an example, they are a fiendishly clever piece of design, performing three operations faultlessly but as a result they are VERY challenging to make and even a blank (if you can find one) needs a lot of finishing before it will do all that is expected of it. Most competent gunsmith can fettle a H&H design but would struggle with Purdey parts.
I also don't like SO guns much. I find them difficult to close in a hurry and the self opening feature has never seemed to be of any great value unless you are opening the gun with one hand whilst reaching for the next cartridges with the other. Fantastic if you are standing under a cloud of birds/targets but not of huge value in my world.