Yay the park is the big sell for UWS for me, bu damn does the FiDi have so much modern convenience.
Craziest thing was sitting outside the NatHis museum in broad daylight and seeing 20+ rats running around in the open.
I love UWS. Zabars, Museum of Natural History, Central Park, Riverside Park, good schools, brownstones, tree-lined blocks, excellent shops and restaurants. Particularly great if you have kids.
FiDi is a different vibe. Very busy on weekdays and very quiet on weekends (I think that's great actually). Seaport is cool. Free ferry to Governors island. Almost all subway lines stop in downtown. Eataly, Whole Foods. Liberty bagels are good. You can walk the Bk bridge.
Both are great choices, you can't go wrong!