Both are fine places to go, I would say the walking/biking is sort of comparable. Lots of trails, plenty of elevation changes but not a lot gnarrr. If you go the moors I guess you’ll be closer to trail centre options at Sutton Bank and Dalby.
If you go the moors you can find quite a few short (say ~5mile) walks that involve a fair bit of challenge and interesting landscapes. Lordstones Country park, Hole of Horcum, Cook’s Monument, Roseberry Topping, Rievaux Valley and probably my favourite bit is around Beck Hole where you can do some fun river valley scrambling that the kids will love. Also steam trains. Any full day hikes are likely to involve tramping over featureless moor.
One plus for the South Eastern dales is you probably have some more options for “attractions”. Fountains Abbey is a great day out for kids, Brimham Rocks, Aysgarth Falls, Richmond stuff like that.