The contrast between the "slow burn" and HIIT interval training is really interesting.
From personal experience, I know that I've lost a LOT of fat while doing a lot of low intensity walking and atkins for about 18 months. However, my muscles atrophied a lot and I lost strength. When I went out on basketball court, I was airballing freethrows.
OTOH - I just can't do high intensity training without carbs. I get exhausted fast and takes forever to recover. Plus, I'm just much weaker.