Oil or water to match

Q: We just had the floors redone using an oil based polyurethane and I’m trying to get the stairs to match. The problem is the stairs were originally done with a water based polyurethane. Do I need to completely sand down the floors or can I apply the oil based polyurethane over the existing water based polyurethane?

Will the oil based polyurethane warm up the wood or will it be dulled because of the previous water based poly?

A: The oil based might warm up the tone in a few years.