One study divided participants into two groups. One ran on a treadmill for 30 minutes 4x a week for 4 months. The other group did only one set of either burpees, mountain climbers, jumping jacks or squat thrusts with 20 seconds on 10 seconds off 8x through 4x a week for 4 months. VO2max was improved roughly the same in both groups. However, muscle endurance improved significantly more in the HIIT group (leg extensions, +40%; chest presses, +207%; sit-ups, +64%; push-ups, +135%; and back extensions, +75%). So, if you're short on time or looking to mix things up, HIIT could be the way to go.
My first response to this study is
Why did you not report the 30 minute cardio test from the HIIT folks?
Obviously, if the one group is strength training only, and the other group is cardio training only, the strength training group would make some gains in strength, while the cardio group would probably not. This study at least negates the whole "HIIT always makes better VO2 gains" mythology. But to be totally fair, they would have to measure the 30 minute treadmill performance of both groups and report that. A really famous HIIT style training Mash-up reports that HIIT alone will give you a spectacular 5K result. If that's true then the HIIT folks in the study should be getting in 4.5 to 5 miles in that 30 minutes. I'd love to see that.
It's also interesting that they tested a "Tabata-Like" protocol of 8 sets of 20 seconds on/10 seconds off. Though I doubt that they were puking in that last few sets, as you would be likely to if it were really "Tabata-Like" with the whole 120% of Max HR thing. I'm not sure I could do that with Jumping Jacks. They also disregard the physical status of all the study participants. Strength gains are usually highest in low-ability trainees. I doubt someone who could do 400 pound squats will quit that and do Jumping Jacks for 4 months and suddenly be twice as strong. As far as the treadmill goes, low-ability trainees could take 4 months just to figure the whole treadmill thing out and make any gains.
When a study is so obviously skewed it most likely has an intended audience of low-information clients. Don't be one of them. HIIT does have an application, and honestly, there are much better exercises for HIIT than these simple bodyweight exercises. Do as many weighted squats as possible in 4 minutes, then go on to bench presses and pull-ups and shoulder presses and rows. Count progress as more weight or more reps. That's 20 minutes of agony that I'm fairly certain would have a much greater impact on your strength gains than hopping up and down waving your hands for that same 4 minutes.