Keep better with tops on or off??
On... especially if you stand them in a plant pot of damp compost... so they don't dry out... if you are using them this week. Or cut off and in compost (clamped) if keeping for two weeks+ :)
I always think that if the tops are left on dug up root crops that the tops are going to keep on taking the goodness we want to eat from the root. So I always chop them off as soon as they are dug up.
The tops die off naturally if they are left in the soil and not dug up at all and if the other creatures do not get to them first, they keep very well .