Why the difference?
Higher ABV on what you're ordering on draft, consumed in a larger format each time (16 vs 12 oz)?
With the case, you're drinking at home and drinking them over a longer period of time? At the bar, you're just downing pints one after the other?
Or - a lot of bars keep lousy tap lines. Stuff that grows in those lines can make you sick in a way that could be mistaken for being even more drunk (headache, stomach upset) and added to 6 to 7 pints (ouch!) might make you feel pretty terrible.
That said holy hell that's a lot of beer at once! Don't forget your DD, and a lot of water!