I wouldn't word it (nor did) "absolute best," but I do really believe that F plays the most "Ries" and works the better functionality wise. (I do main H-Ries after all)
:: H damage is good, but her air throw gives her this kind of pseudo-meaty only in the corner and you get absolutely nothing midscreen unless you sacrifice a loot of damage. However any good H-Ries would know combo ranges and when you can migrate to the corner during a combo for max damage and positioning.
:: Yeah, if H had that 2B, Jesus. But we do have a good DP multipurpose. F DP isn't very good, but they do that an excellent reversal option, 236C instead. Not much of problem using it since you can charge.
:: I think it depends on who you ask from pressure. I think people that might be newer to the game, or just like F moon better in general would favor F pressure. BE236B is actually better for corner pressure because it hits low, is STILL air unblockable and is a bit slower than BE236A so it tends to catch jumps. 624C cancel is reliable but that's 100 meter down, something I'd like to use for damage or 236C/AD when I hit max.
:: F has this and you can cancel it to 236C/AAD. H's allows her to run mixups though, that's why I like it better, you don't need to rely on meter to make using it worth it.
:: Run is godlike, and lets you play the ground well, but the way F plays, its like she doesn't need it. And the way you can use it works for her.
:: Bunker is gdlk, yes.
Both styles work, but there is a reason why H/C is C tier and F is B. I like my H Ries over my F but there are times were I need to use F (only for like 2 match-ups/player personas though). Generally, F is free compared to H, but H has somethings that if you can bring them to life, work extremely well and is why I main H.