It also looks like Leaflet may be focused on geographic data? OSD is not, it has no special geo features (which would be a problem if you need them), but is focused on _images_, which may end up giving it the sort of features (back-end and UI) and API suitable for people concered with high-res images as images, rather than maps. (Does Leaflet actually have facility
for dealing with multi-resolution-level tiling? I would assume so, but it's not clear from a quick skim of the docs...)
Or it could just be that there are multiple products with overlapping feature sets. I don't think OpenSeadragon is neccesarily _newer_ than Leaflet, as I think you imply.
Looks like the first commit in Leaflet repo is Aug 2010; the first commit in OpenSeadragon is Nov 2011. I imagine both took a while to reach maturity. It's also worth pointing out that OpenSeadragon is the open source continutation of an originally proprietary Microsoft product. I'd say they were both developed relatively simulataneously, neither one was developed after a mature competitor already existed.
It does seem from this thread that OpenSeadragon was news to many people who already knew about Leaflet, so I guess Leaflet is better known? A year ago when I was looking for an open JS tiling image viewer, I found OpenSeadragon, and somehow didn't even come accross leaflet!