I have recently* started to tutor in the tuition centre besides my private local and online students.
What are the advantages and disadvantages of learning in the group in the tuition centre? Let's see...

First of all, in the centre where I work(ed), you can book also one to one sessions. That's a plus, but I guess most of the students are using tuition centre for the advantages of group tuition, as if you want to have a one to one tutor, you can simply book them to come conveniently to your home (or in some cases, you come to some other place, either tutor's home or library, or elsewhere).

So what are the advantages and disadvantages of group tutoring in the tuition centre?

Price - you should get an excellent tutor for a better price, as their time is paid also by other students in the group. Definitely positive (for your money management).
On the other side - as it's a group session, you can never have as much attention and focus from the tutor during the lesson (unless the group consists of students of similar age, level and abilities - just like my online group courses), as they need to help all the students in the group. So that could be a potential negative point.
Centres (usually) work with multiple tutors. So even when you have your designated one most of the time, in case your tutor is not available for some date, the centre should easily cover them and provide for you another tutor for that date. Therefore you shouldn't need to rearrange or miss any lessons. That's positive, right?
Depending on the centre and the group, there could be problems with a noisy environment (when not having classrooms, but working in an open space). On the other side - someone may prefer a rather open space as that feels more friendly and it's a nice change from the school environment. Would that be positive or negative for you?
Also if there are students with different requirements in the group, then the tutor's focus on your work is even lower, as you can't work together as a group and discuss the topic together using a whiteboard. But depending on your needs, if you are quite independent and need mostly working on your own and just need checking and a little bit of explanation from the tutor, then coming to the centre will help you to focus and work on your maths, rather than working in your home where there are so many distractions =) And you have still a professional there for you to ask and get help from. So depending on your preferences and what you expect from tuition in the centre, it could be both positive and negative.

As seen above, there are several advantages and disadvantages of different tuition options. It's mostly up to you to decide what's better for you. You can always try and see what will suit you best.

Generally, tuition in the tuition centre should give you more security for less money in terms of having your maths tuition every time you need to. Even when you need to swap some days.

Having a private tutor is definitely beneficial as they're there just for you and will give you more than being tutored in a group (again, unless the group consists of students of similar age, level and abilities - just like my online group courses). But in terms of any sudden changes in allocated time, a single private tutor may not be able to cover your needs. In my case, even when I always try my best, I can't easily swap one student to another day, as I'm already booked for other days. That's why I have "emergency days" free for such changes and that's why I also provide online/distance tuition. But I know it might still not work for everyone. Or when I'm fully booked within classic hours such as weekday evenings (and you don't have time during the day), the only option, if you really want to be tutored by me and don't want for any reason try distance tuition, is to come to visit me in Carshalton in the tuition centre on Saturdays*.

*As time moved on, I moved (literally) too, so I'm not anymore within a reach of this particular tuition centre, therefore I am not tutoring there anymore.