I've a son in year 11 who's been there since year 7 so just coming up to five years. He's really enjoyed his time there and has had few problems. The school is very strong on maths and sciences but weak on English and History in comparison to LRGS. Despite a lot of emphasis on sport, particularly rugby, it's not really a "rough & tumble" kind of school you may expect from a boys' school. There's been a lot of effort put in over recent years to improve the pastoral care so it's been good for a "swot/nerd" kind of child like my son who's not interested in the sports side of things.
Having said all that, I think your DD would need to have a very strong personality/character to be one of the first girls to be admitted, especially if relatively few girls apply in the first year - she could be 1 of only a handful if there isn't much interest - the usual sixth form intake from outside is usually pretty small, maybe 30-40 in total. It's bound to be a culture shock for both pupils and staff as they adapt to the first intake of girls. Some depts are male-dominated in terms of staff, such as Maths, physics, history and english, which also have a fair few "older" teachers who may not be quite so adaptable to female students. My son, who is quiet/shy does better with the younger and female teachers than the "old school" older male teachers.
So, really it depends on your DD's personality, whether she's adaptable to a challenge, and the subjects she wants to take at A level. If she wants to do English/History she may be better at LGGS, but if she's looking at Maths/Sciences, then LRGS may suit her better.
As my son had no interest in the arts, drama, music, etc., I can't comment on how LRGS compares with LGGS at all.