Also, to me, the lottery in general is much more nervewracking. For the game itself, there's at least a decent chance it turns into a convincing win/blowout for either team, meaning there isn't any suspense down the stretch. If we're on the wrong end of that, while it would definitely suck, at least you can gradually prepare yourself for what's happening over the course of the game.
On the other hand, the lottery is publicly revealed so quickly and with such finality and long term impact that it makes it a lot more stressful in my mind.