I don't see how they exert competitive pressure on each other if both networks are free, there's no loss-leader effect as with hardware stuff, and they don't sell any of the same products. Like, 99.99999999999999% of Origin's business is stuff that's not on Steam. The sales of, whatever, Batman or Homefront or whatever that's available on both is clearly a miniscule part of their business. So I don't really see how Origin "competes" with Steam. What are they competing for?
They compete for sure. As you have stated yourself they do carry the same games from other publishers. They both want to build a user base which is more important than anything else. This need to get users does benefit consumers because the stores will try to out sale each other to draw people in.