As for me, I switched from the French competitor Deezer to Spotify in a heartbeat, when Spotify's client totally blew my expectations with zero latency.
So I guess it does help you win the game. But of course it's not the only factor.
I choose Rdio over Spotify because it has a web client which probably means they couldn't leverage p2p even if they wanted to (without using a browser plugin).
That's interesting. One of the main reasons I use* Spotify is because it has a native client and not a web interface.
*I'm actually currently in a period when I listen to music which is likely to never show up at any professional music service, but when I feel the need for mainstream music again, Spotify will probably be my choice for several reasons including the above, despite their recent Facebook-login only policy (which doesn't affect me, but still bothers me a bit).