I've also gotten different advice from different trainers on this. This is what I do now.

Too much running and specifically, too much running at a fast pace gives me shin splints and that sets my training way back. I run twice a week, maybe three times if I need to miss a nightime training session. If I run relaxed, I keep my legs healthy. I'm not at present competitive boxer, I'm not currently running to help me make an ideal boxing weight, just to keep my weight reasonable and keep my overall conditioning up so I can spar more rounds and hold my own against the young guys.

Luckily, I live near a very hilly large park that has paved walks and some dirt walking/running paths. This way I can run at a nice even, 9-10 minute mile pace while still getting my heart rate up. Sometimes I'll do this. There is a very big and steap hill, one of the highest points in the city, and after running a mile, I run straight up that to get my heart rate up, then run another mile around the loop and do it again.

I just started this running program about a month ago after avoiding roadwork during the cold New England winter. Even doing 4 miles, twice per week, in the manner I just described, has helped my stamina considerably. In the gym, I have more wind and can work longer and harder.

It probaby doesn't matter what style of running you do, as long as you do some running and during your running, do some kind of intervals, either by pace or by hills. If I was trying to SERIOUSLY cut weight, I would up my runs to 4x per week and probably alternate between intense hill runs and flat low-heartrate fatburn runs. Sometimes I run carrying 1lb weights in each hand.