Should I replace a sump pump that's not keeping up?
I would favor a strategy that maximizes reliability.  I would go for a pump that is rated at double the estimated worst case flow.  That will mean there is a margin of safety and also mean the pump is not running at full capacity.  This will be better for a longer life, as friction and heat are an electric motors worst enemies.  This may be hard to estimate, but double the GPM (gallons per minute) might be a good starting point.

Take care that the larger motor is within the capacity of the circuit.  50% of the maximum circuit capacity is a good rule of thumb, especially for a motor circuit, which has large start-up current requirements.  Since this circuit is so critical, it would be advisable to make it a dedicated one, ensuring no other device would cause a nuisance trip of the circuit breaker.

Finally, large rain related increases in sump flow might suggest some runoff improvements around the house might be in order..  Extending downspouts, berming any reversed pitch areas (places near the house that collect water).