Did your daughter pass @troppibambini?
I have 2 DDs - one already at AGGS and one who will start next Sept. My DD is very happy there and I have certainly never heard of girls being withdrawn due to bullying. When my older DD started, there was a general impression given by the school that any girl who attended there was extremely lucky, and as such, any queries or attempts to engage with the staff were brushed away as not really important - the school knew what it was doing and so why would they need input from parents?! It feels less arrogant now, but I think its a slow change. They do offer a whole range of opportunities and the results are outstanding - I think if you're voted as the best state school in the country, it's probably difficult to be humble about it.
I also know girls who go to Withington - all happy there too. I agree it is an amazing school. I think there is more willingness to engage with parents (although that's just a perception, no personal experience), but that may be because you're paying for it! I think class sizes are generally slightly smaller, its a much smaller cohort but both schools are highly academic, single sex so very little to choose between them. One thing I did notice however from visiting the schools is that Withington and MHSG have a really strong alumni presence - lots reunions, girls coming back to give careers talks. I get the impression (and again its only my impression) that the smaller cohort means that it feels more of a community that goes beyond school.
I would consider the distance to school, whether you have a sporty girl (think AGGS is better for sport), and how the cost would impact on your family (do you have other children who might follow her)? You're looking at £100k even without any fee increases or extras for 7 years so its a big financial commitment if you have the choice of a "free" education locally too.
Good luck with your decision.