The Maggie's Fitness for Life program includes both. Still, we tend to agree that calisthenics classes offer more bang for the buck (or for the time.)
The logic is that 50 minutes of intense calis (with maybe only 6-10-second breaks between routines) is a good heart stressor while also working on athleticism, balance, flexibility, light-weight endurance muscle work, and body-weight exercises. In addition, most calisthenics classes include specific HIIT routines like rowing sprints. Obviously, each person works at his or her own level.
Some thoughts about it here.
If you take three tough calisthenics classes weekly, do you need to do your own HIIT cardio? Maybe not, because calisthenics classes that keep your heart rate up are stressful cardio. It depends on how intensely you want to condition, and on how ambitious you are. What sorts of circuits do typical calisthenics classes include? Rowing sprints, kettlebell swings, pushups, jumping jacks, jump rope, heavy ropes, body weight squats, heavy ball throws, sandbag slams, floor and core work like planks and crunches, hand weights, stretches, etc etc. Fun stuff, never boring because the routines are only 30-60 seconds each.
We do like the idea of one "long, slow" cardio hour, like swimming, jogging, high-incline walking, stair machine, etc as a recovery day from a week's exertions with heavy weights and calisthenics. There is evidence that "active recovery" like that makes for more effective physical recovery than doing nothing. A 4-5-hour hill hike is a perfect recovery activity from demanding workouts.
With calisthenics, the less spare fat you carry, the better you will do and the more quickly you will move. To shed spare fat, cut the food volume and get rid of those carbs. (Our readers know what carbs are: fruit, juices, grains and grain products, beer, root vegetables, anything with sugar, etc.)