John Ratey (http://en.wikipedia.org/wiki/John_Ratey), the professor of psychiatry at Harvard Medical School who wrote Driven to Distration, recently published a book called Spark: The Revolutionary New Science of Exercise and the Brain (http://www.amazon.com/Spark-Revolutionary-Science-Exercise-B...).
Spark details how high-intensity cardio (like sprints or interval training) put your brain chemicals in balance in part by generating BDNF (http://en.wikipedia.org/wiki/Brain-derived_neurotrophic_fact...), which as Ratey describes, it's like "Miracle-gro" for the brain.
Last year my stress levels were getting out of control from working too much. At the time I was running at least two miles every day so it's not like I wasn't exercising. But then one day I changed from running a couple miles to running 50-yard sprints, as fast and as hard as I could push myself. The first day I only ran four sprints, but I felt euphoric the rest of the day -- the best I had felt in years. So I tried it again a couple days later, and sure enough it worked again -- I felt amazing.
So then I had to find out why this worked -- why a few sprints were so much more effective than running several miles. I started Googling and eventually found Ratey's book -- it explains the entire biochemical process of what's going on and why sprinting works.
It's an eye-opening read. Each chapter covers how high-intensity cardio affects things like stress, anxiety, depression, ADHD. I have ADHD but haven't taken anything for it in years (since I was in college), and I can attest that sprints not only fixed by stress levels, but my ADHD symptoms were almost non existent.
Here's a key point that Ratey makes throughout the book that completely changed my perspective on things -- he says that instead of thinking of exercise as something you should do to look good and build a healthy body, you should instead think of exercise as the key to building a healthy brain:
"We all know that exercise makes us feel better, but most of us have no idea why. We assume it’s because we’re burning off stress or reducing muscle tension or boosting endorphins, and we leave it at that. But the real reason we feel so good when we get our blood pumping is that it makes the brain function at its best" (http://www.sparkinglife.org).
In the book's introduction he goes on to say, "Building muscles and conditioning the heart and lungs are essentially side effects. I often tell my patients that the point of exercise is to build and condition the brain."
In fact the brain exercise routine he recommends is similar to a weight workout routine, in that you have to push yourself hard one day, and then take a day off to let your brain recover, just like in weight training. Another key is when you sprint, always put everything you have into it. Run as fast and as hard as you can so you are constantly pushing your body and your brain past their limitations -- this is the key to growth.
Sprinting is anaerobic training, as is most strength training. It's high intensity, you can't sustain it over a long period of time, and it makes different energy demands on your body than aerobic training does.
With that said, I much prefer anaerobic training. It's more fun, for me. And if you do intervals over a long enough time, you're also increasing your aerobic capacity.
When I train jiu-jitsu, I do several rounds of live rolling. Usually something like 4 6-minute rounds with a minute rest inbetween. The hard part of live rolling is the anaerobic part: quick spurts of high intensity. How fast you can recover from them, and how often you can sustain doing them over time determines how well, athletically, you will do. But this is also a 30 minute period with an elevated heart-rate, and you never are fully rested inbetween your anaerobic bursts. So, it is also an aerobic workout.
Despite not doing much explicit cardio training, I still have the cardio capacity to run decent distances with decent times, on the rare occasions I do. That's because I am training my aerobic system even though most of the exercises are anaerobic. (I once went on a 9 mile run having not gone on a run in over 6 months, having only done jiu-jitsu training and conditioning during that time. My lungs were fine. My legs were not.)
If your sprint workouts involve sprints with very light jogging inbetween then you will work both.