Why is Na6xc7 better than Qd8xc7 (From the Stappen Methode)

Here is a problem I need help with:

I see Na6xc7 and Qd8xc7 as equally valid. The solution claims Na6xc7 is superior and stockfish agrees.

Why should I keep my Queen on d8?

My reasoning: Qc7 deploys the Queen instead of having her stuck in a box. Qc7 also directly threatens White's Queen.

I understand white is threatening an attack on h7, but I have a problem seeing the difference made by having the Queen on d8.

Does anyone understand the fundamentals of the position?

Suddenly things are starting to make sense when I look at what stockfish is trying to do as white. 

I now understand that Qxc7 creates a weakness that white will subsequently try to exploit. That was the missing piece!

Thank you!

Indeed, the first thing I see when looking at the 1...Qxc7 move is that discoveries with white queen are possible. 2. Bxh7+ and 3. Qg6 with tempo leads to black getting under heavy attack on the king. There is also some wonky stuff with 2. Qa4, although I'm not sure if it leads anywhere, since 2...Qb7 seems to defend everything.