I'm in Italy and some of my students go to the Bocconi every year. I have 3 doing Economics at the moment, and two more will be going this year.
Thing to consider more than anything about Italian university is that it's a whole different experience.
There's no real pressure to finish, there are generally various dates available to do the exams (almost always only oral) and the student chooses when to do them. There tends not to be the same teaching staff-student relationship that happens with UK universities.
Within Italy itself, the Bocconi is of course highly regarded, (esp business/economics etc) though as it's private there is the idea that once you're in, you're made. Because it's private there is more pastoral care regarding the academic element but virtually nothing for non academic. That's just how Italian university is.
Have they been accepted for a triennale? If so, then it's a given they'll have to do a further 2 years for a magistrale. This isn't the same as a master's but a sort of add-on. But an add-on that everyone ends up doing. That might also be worth factoring in.
My daughter chose a UK university over Italy as she wanted the UK university experience. When I talk to my students here about the experience she is having in the UK they say unanimously "it's a whole other world".
I'd say between St A and the Boc it boils down to if you want to get your head down for 3 years, eat in nice restaurants with fairly rich peers (you have to be a wealthy Italian to be able to afford the Bocconi) or have a traditional uni experience as we know it in the UK.