Oxford MFE or LBS MFA

You will learn more at Oxford but you will have more fun at LBS.

In terms of academia, MFE has been around longer and of course you have the Oxford brand. Given that you are such a high-achiever, academically speaking, an Oxford MSc would allow you to pursue a PhD at a later date if you wish to do so. I don't know if they've changed things with the MFA (it's such a new programme) but the MiM at LBS is, by the school's own admission, not academic enough to be considered a springboard for PhD.

Social life is better at LBS, hands down. Oxbridge have postgraduate only colleges. You will most likely end up at one of those and even if you don't, you will have to go out of your way to mingle with undergrads. Everyone at LBS is postgrad but the social side of things will be like fresher week every week, apart from recruiting season of course... Even if you ended up making some BFFs at Oxford, where would you go out? LBS is in London. There will always be something to do but you will be broke all the time though.

For an average person whose goal is to collect prestige brownie points and advance their career at all time, I would suggest Oxford MFE. In your case however, I would suggest LBS if you value the social side of things and if you really want to do an MSc now.

Have you considered taking a gap year? With your profile, i'm sure both schools will be happy to defer your admission another year or two even. When it comes to recruiting, your young age can (but not always) work against you. Take some time off. Travel. There is no rush to get ahead in life. You are 18/19, it is so easy to explain that you wanted some time off to see the world or 'find yourself' or whatever. It is much harder to take a career break 5, 6 years down the line and at that point you can't really go do an MSc anymore as you've already done one.