There are plenty of different types of training, they can range from hypertrophy to fat loss etc. I’m going to explain to you how these different types of training methods are performed better with a mobile personal trainer vs a gym personal trainer.
If you are training for muscle mass (hypertrophy) or weightlifting (trying to pull a PB deadlift) then a gym personal trainer is usually more suited to you, as they have the access to heavy weights and all different resistance machines in the gym. A mobile personal trainer doesn’t carry around heavy weights and all different resistance machines as its impossible. So therefore for these types of goals a gym personal trainer is Better.
A mobile personal trainer is perfect if your looking to lose weight, tone up etc as they carry around enough equipment to make the session fun and enjoyable. To perform this type of training they can do it in all different types of location e.g home, office and local park. They are ideal if you find the gym an intimidating place, you want the trainer to come to you rather than you go to them or your just trying to get started and want to learn the basics and feel comfortable in your surroundings.
The bottom line is, it all depends on goals and what your trying to achieve.