They’re normally rather well built, but industrious with it, judging by their extensive sett excavations.
They've been known to be very tenacious per your own contradictory example (very very lazy, but coursing a hare like a dog) - they’ve been seen seen following the milk scent from a lactating hare back to the leveret, for that leisurely lazy supper.
Opportunistic might be a more apt description?
For certain a pair of foxes can have a large family, and occasionally a couple of litters from different families will be raised in a den ( or an abandoned badger sett, for example

), but after the summer the fox cubs tend to go forth and disperse, and try to find a territory to call their own, whereas by and large the badgers are content to continue to stay in the area playing happy families, leading to building up of the population density rather than wider overall distribution.
Regional variations will doubtless apply.