This is a common question, and it has a common answer. 95% of the time, the answer is no.
New pool pumps are more efficient, and have better designs, allowing more water to flow per horsepower than older pumps. Providing that your pump was originally sized properly, replacing with the same amount of horse power is usually sufficient.
When a larger pool pump is installed with the same piping and filter used, the pressure in the pump will increase, along with the electrical bill. The filter is put into overdrive, but does not clean any better or faster.
For the same price as a larger pump, you can purchase the same size pump as your existing pump.