its very simple. There are two types of damping Mechanical damping: where when speaker cone excites and left then if its taking more time to damp then you need external damping control from the amplifier and hence you need higher damping factor amplifier.
Higher mechanical damping means you dont need much to control the cone but a modest damping factor is sufficient.
See first if your woofer cone is moving freely without much effort and then decide which amp to go with. Damping factor about 10 to 50 is considered as low DF.
50 to 300 is commonly observed.
300 to 500 is high
500 to 2000 or 4000 is very high ( usually subwoofers requires more damping factor to control the heavy cone )