Just replying to your query as no-one else has, and I was in exactly the same position (for myself) forty years ago!!!
Which does your DD prefer? My parents let me decide and I chose MT because, like your DD, I was very bright and consequently liked the purposeful, hard-working atmosphere there. It worked out well for me as I ended up at Oxbridge.
Obviously I know very little about either school these days, apart from the glossy, colour magazine I'm sent from MT every year which shows the school clearly still has a very vibrant atmosphere.
Interestingly we've been in a similar predicament for DS2 recently. He's currently at a grammar school but for various complicated reasons will be moving to a boarding school for Sixth Form. He's extremely clever and had a choice between a well-established, business-like, large-ish school with lots of activities on offer, or a more up-and-coming smaller school with a fantastically nurturing, family-like, holistic environment. I thought he'd chose the latter because everyone there was so incredibly welcoming, but he hasn't. He says that it's so important to him that he does well academically that he needs to be somewhere where he knows he'll be pushed and there will be other children of a similar ability to him.
I suppose it depends whether your DD wants to be a big fish in a small pond, or a small fish in a big pond. There isn't a right or wrong answer, it's just a question of what will suit your DD.
Good Luck in your decision-making.