It appears to be dependent on how much time the station engineer has to tinker with the processing to try to match equalization and levels. And the delay to match analog to digital.
HD's a maintenance hog so it tends to be neglected, since nobody's listening in digital anyway.
Being an engineer at today's group station-clusters acquaints you with the medical concept of "triage." The first task is to sort out and prioritize the tasks. If you get to the end of the day doing the important stuff - the time is all gone - you have a choice between (a) fixing the stupid HD stuff for the Nth time, or (b) going home, getting something to eat and sleeping a little after a 16-hour day (and you've been awakened in the middle of the night with emergency calls three times in the past 10 days.)
Guess which one's gonna happen?