I'm not going to compare eras...but the athletes playing in the NFL today are in a completely different stratosphere on all accounts. It is a significantly faster game with some of the most elite athletes in the world playing. Unitas would be in way over his head as would anyone who played decades ago.
Who's to say Unitas couldn't adapt in if he had played in this era from the get go? Or even been better? I saw him work with guys like Chris Redman at UofL and even at an old age had a good grasp on reads and etc. I think you're underestimating his talent.
Ironically, he was 6'1" and 194 lbs. About the same size as Brees give an inch and a couple pounds. I don't think it'd be unheard of to say he would be capable even today with the same training.