I feel legs gives more stability.
This is the main reason I chose a pedestal. Otherwise, its just a matter of preference. This pedestal mount is completely stable. I don't think that's an issue.The Pedestal can hide an OAK where you come up through the floor inside it on some stoves but I am a bigger fan of legs.
It seems I heard somewhere that some stoves require a higher r value hearth pad with legs versus a pedestal? My stove particular I liked the pedestal cause it sat higher and hid the oak.Legs all the way unless you have something to hide and one less thing to clean.