I think it depends on the goal of the workout. If I am doing a medium-pace workout, like mile repeats at 10-20k pace, I will do a short jog rest that specifically isn't a full-on "rest" period, because I am trying to simulate a longer, more moderate effort.
If I am doing intervals at 3k-5k pace (be it 400s or miles, or anything in between), I will often walk the first half of the rest and jog the second half; the walking allows for more recovery, but the jog keeps me warm and loose.
Acting like jog rests between intervals are worthless (like a previous poster did) is absurd; it depends on the rate of the jog and the length of the jog. Sure, "jogging" at a walking pace might not be much different than walking, but jogging 200 or 400 meters at easy run pace between tempo reps sure as hell counts just as much as a regular easy run would.