Is the fastest solution for one NP-Complete problem the fastest solution for all NP-complete problems?
A polynomial-time reduction only needs to preserve the size of the problem up to a polynomial upper bound (which is implied by the time constraint).
As an example, suppose you have two NP-complete problems and $A \le_p B$, the reduction blows up the instance size from $n$ to $n^2$, and $B$ admits an algorithm with running time $ 2^\sqrt{n}$. This only induces an algorithm for $A$ with a running time of $2^{\sqrt{n^2}}=2^n$.