Thank you for your question and please also see the article I wrote on frozen shoulders here.
Wrt the surgical treatment, MUA is basically where you are anaesthetised and the surgeon manually moves your arm to break the adhesions. There is a the risk of other trauma to the shoulder but it is an option.
The arthroscopic approach requires more finess and surgical training/experience. This is where the surgeon uses a minimally invasive approach to then cut away at the adhesions from within.
Usually in our centre we try the hydrodilatations and physiotherapy before moving onto a surgical approach and in general our surgical need has leases end due to this minimally invasive injection technique.
So what is better? It depends on what your surgeon and centre are able to provide! Both have its merits and risks and it needs you to decide with your surgeon what you want to pursue.
Bw
Dr Dinesh