Do shots of beer get you more drunk than drinking beer?

That all depends. The level of drunk you get depends on volume and time. If you consume a beer over an hour from standard drinking, and consume a beer over an hour through shots, they could have the same result. But if you do shots to consume the beer quicker, like shotgunning or playing century club, then yes.

If your goal is to get drunk, don't waste dishes by using shotglasses, just chug your beer.