The way that he reminds me of Brady is because he is smart and by all accounts extraordinarily coachable, you don't have people like Parcell rave about his intangibles if that isn't the case.
I've watched him in the 2014 and 2015 Florida State games, and now in the Miami NE game. That isn't very many data points (is anyone on this board a NC State fan that watched all of his games??), but I was struck by how much his game evolved and changed year to year. In the 2014 game (I watched the whole game, but attached highlights only below) he looked he was routinely shrugging off defenders and throwing it down the field with defenders hanging off of him, and repeatedly bulling ahead on runs, he isn't super fast but he is a smart runner, and looks to be strong as an ox. Look at the play at the 1 minute mark where he shrugs off defenders and throws the touchdown (!), and the play at 1:43 where he throws while going down(!!), doesn't that remind you of a poor man's Roethlisberger? I mean skill wise, not intangible wise.
The only summary I could find of the 2015 Florida State game is 15 minutes long, I have linked it below, but I watched the whole game. Surprisingly, I thought his game had evolved into something much different. He appeared to be much more under control. If he got wrapped up while passing, he would go down instead of trying to extend the play. He still ran, but more under control. He threw the ball away much, much more often. Was this him being coached to protect the ball better? It looked like that to me.
https://www.youtube.com/watch?v=BffqboBTGPY
Then, there are his Patriot highlights, once again his game looks like it has evolved tremendously. He's throwing these short passes with a couple of step drop back, quick release. No running all over the place extending the play. When he ran, he actually slid down (!!!), which is completely different, in college he would try to bull over people.
So back to your original point, one way he is like Brady is that he is super coachable, I think you can tell that by looking at how his game evolved from 2014 to now.