Travellers tend to gravitate to London as it obviously has greater availability of work but just living there will eat up your savings pretty quickly.It really is an expense place to live. I know a lot of people who have gone to London and don't see much of the England/Britian as they either can't afford to travel as much as they want or they just get caught up in all the London has to offer. If you live outside London you will be more likely to explore more of the country. I have been here 4 years and hardly ever go to London as I find the most interesting placed in Britain are in the country, not in London.
And if you want to see London you can get cheap flights down from Edinburgh.
I have lived in both Edinburgh and London and:
Edinburgh is a nicer place than London and more picturesque. It gets really busy during the festival which is fun for a while then gets annoying. Wages are lower than London but the cost of living is a little lower (though less than the rest of Scotland).
There is always lots going on in London and loads to do, though it is so expensive to live in that you don't really end up doing half of what you would like to. Wages are higher though so if you sit in and eat pasta and live near work you can save quite a bit. London is overcrowded and polluted. Transport links to the rest of the country are really good, so its a good place to travel from.
I think both places are better to visit than to live in.
I now live in Brighton which I think is a better place to live than either!