So, we all have different life/work schedules, and for some (if they have the time and the means) depend heavily or sometimes exclusively on private training sessions to learn jiu jitsu, rather than take a group class. I really have maybe taken about a handful of private lessons in my jiu jitsu career, and I think there is definitely a benefit to each side.
I do however compare the two in this fashion- privates are more like tutoring, whereas taking a class is just like, well, taking a class in school. There is a definite benefit to taking privates, especially when it is really your only opportunity to train. I think of a group class less like the traditional desks and chalkboard and more like a multi-age, Montessori classroom.
Just in case you have no idea what I am talking about, Maria Montessori was an Italian doctor who developed (or furthered, I imagine she was not the first, I am not sure) a teaching method in which children in age groups, roughly in groups of 3 ages, are encouraged to interact with their classroom, and more importantly with one another without the use of desks. Not just learning the subject matter, but they also learn how to interact with one another: the older children become mini-assistant mentors, feeling a sense of responsibility towards their younger classmates, the younger ones pick up one social cues and protocol from the older ones, and everyone cooperates with each other on the general premise of respect and concern of the well-being of one another.
This is all just the theory: I’m sure there are many people out there with horror stories of this sort of class set-up gone horribly wrong, but that’s not the point here. The point is jiu jitsu group classes sort of operate on the same theory- you learn not only from your instructor, but also from your fellow students, who can teach or at least remind you of different details of techniques during class: older students feel a sense of responsibility towards the newer belts, and while teaching while the main instructor is teaching, they do from time to time become those mini-assistant mentors as well. All of this (again, at least should) foster a sense of camaraderie among the students. And, you also become more acclimated to training with different body types- tall, short, thin, stocky, etc.
Privates on the other hand are like being tutored: you are going to someone who has mastered the subject and you are getting an in-your-face, one on one instruction. This can be great especially if you are having difficulty understanding a concept and need the help of someone who has much more experience than you do, but at the same time you miss all the benefits of the group class atmosphere, and if you train exclusively with privates, there is a good chance you are missing the community atmosphere that is built with the rest of the students in the academy. That, and you are primarily training with one body type, and someone who is probably going a little slower than they usually would, to ensure you execute the technique while training.
So, my feeling on the two is pretty much this: group classes in my opinion are preferable for obvious and non-obvious reasons, and privates are great, but shouldn’t be your primary form of learning techniques, if you can help it. Again, for some it’s the only way they are able to train and it’s better than nothing, but everyone should try to make a group class, at least occasionally.