I think a combination is the ideal way. Yes HIIT is more effective techniqcally but long duration low intensity exercise is an easy, low impact way to keep from being lazy for days after a grueling workout with intervals (active recovery really).

But HIIT is not automaticaly high impact. Why not use breathing squats? swimming? cycling?, barbell complexes?

Also, the volume involved in HIIT should mean a quick turnaround on recovery times.

If your joints are sore from a sprint drill session, then rest! Phase it so that your upperbody lifts follow over the next 48 hours, or work on your mobility/core stability instead - dont go jogging and doing empty cardio that will only serve to hamper your adaption to the HIIT

Good point Cord.

I have to agree with you.
I've been doing HIIT for a short while now, (about 3 months) actually for the first time in my life, and the fat is literally dropping off faster than I could have ever thought possible. I went from 230lbs. at the 1st of the year down to 192lbs. as of this morning.
I'm at the point now where people are noticing the weight loss, and asking me what I've been doing to lose it.
One thing that I've been doing lately is incorporating a sort of HIIT in with my forms practice. I'll do a form, then 20 pushups, then another form, then 20 crunches, form, pushups, ect...
Also, I'll do a giant set of 30 jumping jacks, 30 pushups, 30sec of running in place with knees high, and 30 crunches, then repeat it twice more for 3 giant sets with 20 seconds rest between each set.
I'm sweating bullets after that.