The benefit of workout with a home gym is found to be hugely profitable for those who know what exercising is all about. By training the entire body as a single integrated unit, you can stimulate the same muscles during one workout that could require two to three isolation-based workouts. For instance, you are combining exercises using your upper and lower body, as well as your core, into a single workout. In a total-body program, you usually do just one or two exercises per specific muscle group in one session.
When using a total-body training approach with a home gym, however, you only do one or two exercises per muscle group, so you can easily switch things up, whether it is going from full-body training to full-body training, or from month to month. You are going to have at least a day of rest in between every full body workout, so the full body workouts are going to allow the muscles to have the most time to recover. Full body workouts are the perfect training setup to lose fat, as it gets you working for every muscle group at least twice per week, yet does not demand too much from the body from a recovery standpoint. Depending on how you structure your full body training programs, you might find that they require slightly more time at the gym to get through, but when you factor in the total weekly time commitment that they require, you are still going to come out far ahead compared to other programs like an upper/lower split.
A 4-day workout works much like your 3-day workout, except each day will spend some time doing lower or upper body exercises. In the example above, you have got a good mix of hard, full-body exercises, stable-state cardio, and muscular isolation workouts over five workouts. You can certainly incorporate both full-body exercises and muscle isolation movements into your training regimen if you would like - and if you are smart about planning, or you get a good program from your adviser, you could even do them both in one workout. That way, you can incorporate total-body workouts around your busy travel schedule without missing a beat, or focus on other workout activities such as swimming, biking, or yoga, without sacrificing strength training.