Consider the position before 15. Nc4.
[FEN "r1b2b1r/ppp1k1pp/8/4p1N1/4P2n/1B1q4/PP1N1PPP/R2Q1RK1 w - - 0 15"]
You have developed two knights, a bishop, and castled. Your opponent has developed a queen and a knight, and his king is stuck in the center.
In other words, you have a massive dynamic advantage! You are already in position to leverage your superior development & king safety and steamroll your opponent off the board. There are plenty of ways to do so - Rc1, Qc1, Qh5, they all produce immediate threats against your opponent's king that are hard to fend off. These moves even come with tempo because Black can hardly allow Qxc7+ or Qf7+.
Nc4, on the other hand, allows your opponent to trade queens. When you are on the attack this is one of the things you least want to do, because the queen is the most powerful piece and hence also the most powerful attacker. After 15. Nc4 Qxd1, you still have a comfortable advantage, but you are no longer playing for immediate checkmate.
I haven't looked at the computer's suggestions and it probably sees something more concrete, but still: on general grounds, trading queens in this position is a bad idea. By extension, that makes Nc4 an inferior move.