I'll try this. I would say the chances of failing are obviously much higher in the first case. But there might actually be no more 'pressure' because you've been brought into an obviously tough situation and left with someone else's mess.
In the second situation, on paper it's relatively easy, but the other team might well use one or two pinch-hitters. And if you allow a man on base you will be facing the top of the order.
Also, how does the fact that the batting order doesn't matter that much, statistically speaking, factor into this?