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You really have to compare datasheets.  There are some general differences, but you shouldn't go by those in specific instances.

MOVs usually have softer knees, are available at higher voltages, and are available for dissipating higher powers.  Usually.  One drawback of MOVs that they get "used up" a little bit each spike they absorb.  On the other hand, they may be available at temperatures where TVSs can't go.  Another parameter to consider is off-state leakage, and how that varies over temperature.

Again, look at what's available for your application.  What is your threshold voltage?  How much current must the device be able to conduct to clip the voltage?  How much energy must it be able to dissipate each spike?  Does off-state leakage matter?  What temperature range will this need to work over?

Once you have candidates that match all your criteria, read the datasheets, check the prices and availability, and compare.