Both. I record both.
Since that ties up the two live feeds in my living room DVR, I'll watch something recorded on the DVR itself for approximately 1 - 1.5 hours. Or noodle online for that time period (avoiding sports websites).
Then I watch the B's. With the time saved fast-forwarding every commercial and intermission between periods, I nearly catch up with live play. Which is before the Sox's have ended.
Then I do the same with the Sox. Baseball has even more dead air than hockey (between innings, switching pitchers, 7th stretch blah blah), that I only stay up slightly later than if I had watched the game live from the beginning. Sometimes I even catch up to live play on the ball game too (especially these long WS games).
I have the same set up running in the bedroom in case I get tired. Sometimes I'll finish a game (usually another hockey game) in bed. I've finished conflicting sports programs the next morning with coffee before I put on TV or DandC.
I'm seriously thinking of switching to the Hopper which has even more feeds and recording options. I'm not crazy about their compressed signal on my TVs though.