Many, actually. Both are distributor, have friends, chat, and overlay function. Both are also free to use provided that you own a game on their platform. Steam, however, requires you to make at least 10USD purchase before your account is fully activated.
AFAIK, what Origin don't have are those communities, groups, badges, custom profile pages, Big Picture, VR games, hardware surveys, user reviews, mobile app, library sharing, in-home streaming, logging in on multiple device (else, In-home Streaming would be useless), video streaming service (EA uses Twitch), forums (EA has forums of their own, but usually for EA games and Origin).
So, yeah. There is that much difference between Steam and Origin.