Since 2010 the Broncos have drafted the most QB's (7). Two in the 1st round, two in the 2nd round, and three in the late rounds.
The Browns have drafted six QB's. Three in the first round and another three in the 2nd-3rd round. The Patriots have also drafted six QB's but none in the 1st round. Two were in the 2nd and all the rest were later picks.
The Cardinals (2 in the 1st), Titans (2 in the 1st), Jets (1 in the 1st), Jaguars (2 in the 1st), Eagles (1 in the 1st), and the Bills (2 in the 1st)....have all taken five QB's in the draft since 2010.
I might say the Patriots have been smart. Not sure I'd say that about the rest. Pretty much, you go get a QB and stand pat until you have to go get another one.....or you make half a** attempts to get one year after year. If you are astute maybe you draft a QB and flip him for more.