I’ve used all of the above. No expert so others may have different views, but I found the following:
Purgatorys were Control versions. They are lighter and faster rolling, but they folded and burped all the time (25psi on Flows). Sidewalls noticeably thinner than Maxxis EXO. Grid versions may be better? Very good overall grip though.
Maxxis DHF on front and rear for me for keeps. Fast rolling and tons of straight line grip, which has been ideal over winter. Typical ‘slip to grip’ Maxxis when cornering hard but not (yet) managed to wash one out. Had a DHR2 on the rear for two rides recently and found it was gripper than a DHF on the rear, and slower rolling, but gripped amazing. Too much rear tyre for me so swapped back for DHF. Dare say DHR2 would be great on the front, very similar to HR2.
HR2s I found slightly slower rolling than DHFs but very good all rounders. Cornered perhaps a little more consistently but slightly heavier. All Tyres were in 2.3, though the Specialized I think were a pinch smaller.