1PPS vs high resolution timer in CPU
You will want to "discipline" the local timer with a PPS from an oscillator with better long term stability (I infer GPS from your questions tags). This can be done by measuring the "run away" (if using a 1GHz precision timer, does the PPS always occur after 1,000,000,000 ticks?) and tune the local timer to compensate this runaway.

The added value will be improved long term stability. 

The GPS is not "better" than your local oscillator, nor is it the other way around, because the stability of oscillators is not a simple scalar value. It can be measured by plotting the Allan Deviation against integration time in a sigma-tau-diagram. Given two different oscillators, one might be more stable on the short term (crystal), the other on the long term. In this case, the lines will intersect in the diagram. The abscissa of the intersection gives the optimum time constant for such a control loop.