The only thing that was being compared in the OP was the frequency of passes thrown by distance and their completion percentage, showing that the lack of deep passes (and the lack of passes thrown behind the LOS) is most likely a function of the offensive system and/or the receivers and not any particular preference or abilities of the two quarterbacks.
That's true in general, but it's misleading. Quarterbacks tend to have greater success in games that they win than they do in games that they lose -- and winning or losing typically depends on how much success they have (especially compared with how much success the opposing quarterback has). Quarterbacks also tend to have greater success against weaker opponents (making those games more likely to win) than they do against stronger opponents (making those games more likely to lose).
But quarterbacks that win a game typically are MOST effective throwing when they are trailing (107.4 passer rating over the past five years), followed by when they are tied (100.9), and LEAST effective when they have the lead (99.6). Likewise, quarterbacks that lose a game typically are MOST effective when they are trailing (77.5 passer rating), followed by when they are tied (75.1), and LEAST effective when they have the lead (70.6). So as you say, comparing apples to apples (the same quarterbacks in the same games), quarterbacks actually tend to have greater success throwing while trailing than while leading.
In other words, playing with a lead DOES NOT "make" a quarterback more effective -- on the contrary, having success in the first place (whether ahead, tied or trailing) is most likely WHY the quarterback is in the lead.
