I don't own a Delica 4 or a Persistence, but I own an Endura 4 and a Tenacious. Similar enough. I voted Delica 4. The main reason why I prefer to carry my Endura 4 over my Tenacious is the closed-back handle, because it is a backlock and thus the lockbar acts as a backspacer, sealing off the entire back of the handle. Chuck the knife in your pocket with a bunch of other stuff and nothing's going to get between the handle scales and come into contact with the cutting edge of the blade. The downside is pocket lint may accumulate in there, best to have a squeeze-blower to blow it out every now and then. Open-back design doesn't accumulate so much, so there's really pros and cons to both open-back and closed-back design. But I blow out my knives regularly as a habit so the closed-back design's cons don't really bother me.
Considering my preference for the Endura 4 over the Tenacious, I'm pretty sure I would likewise prefer the Delica 4 over the Persistence.