Pokemon Online requires download to play, while Pokemon SHowdown doens't but has a download feature anyway.
Pokemon Online saves things to your computer (eg. battle replays), Pokemon Showdown uses internet for saving your stuff (i'm not sure about if you download it though)
Pokemon Online has a motto you can make for your profile, and some other things.
They both vary on tiers and whats allowed in them.
I think that's the only notable differences between them, other things are just appearence, music, etc. I personally prefer Pokemon Showdown. If there's more i'm not thinking of then i'm sure another user will come along and correct me.