I've run into this issue as well since some writers can be adamant about being public or private. I do groups but am more known for 1x1s and I prefer things public. I don't read RPs and I don't expect mine to be read either. Why I keep things public is because it's easier to keep track off. And say I'm offline but on a private browser lurking, I can still see if someone posted and read it when out and about. If I had something in PMs, I wouldn't be able to keep stalker tabs on my ongoing RPs. Those are my main two points. I forget PMs far too easily and it makes looking at them offline for any progress, easier.
Now sometimes people are shy if say the content is entirely smut and while this site prohibits it being public, some sites are solely based on such themes and even then, people have been known to shy away from displaying threads publicly.
So it boils down to comfort and personal preference. I think it's easily to be public and also lends itself well to logging post samples for others to see, should someone want to check out a potential RP partner's typical posting habits.
Those are my thoughts on the matter but I am interested to see why some feel better doing things in the dark shadows. :3