These are personal points of view so use them as you wish!
Caulerpa uses rhizomes (roots) to trap and extract sediments, so each time you harvest, you are disturbing the substrate of your refugium and it runs through your main tank.
Caulerpa can go sexual and release toxins back into the tank.
Caulerpa can be very invasive, so if a portion made to your main tank and settled and started to grow, you could have the problem of trying to maintain it in your main tank.
As you probably have noticed already, the chaeto does not attached to anything, so when you harvest the overgrowth, you are not disturbing much.
Chaeto also has not been proven to go sexual.