Well, I will tell you my opinion, since a good friend of mine took the MSc in Management at Imperial College last year.
First of all, bear in mind that every brand new course (like both you have been accepted to) is going to be a little unorganized. This affects more the Warwick MSc, because the first intake will be this year).
First of all, my friend thinks that the course of Tanaka is quite good, a bit theoretical though (I suppose that the Warwick one will be more theoretical). Tanaka Business School is a very good business school. Probably there are a few better one in terms of Business Schools (like: LSE, Oxford, Cambridge, LBS, Manchester, Warwick) BUT if you consider the reputation of Imperial College, I believe that you don’t have anything to think more… Your degree will be from Imperial College, one of the best Universities in the world!
Many will say that the business employers know about the business schools and can distinguish the very good from the good ones. Well, my friend told me (you can double check it of course) that MANY top employers were seeking graduates only from Oxford, Cambridge and Imperial, because according to them, only these Universities create graduates at the top level.
Another thing you should consider is that you have to choose between London and a city away from London. In London you have far more opportunities to search for jobs, attend interviews etc. Furthermore, London experience is one big pro! On the other hand, the cost of living in London is quite high!
Lastly, the most of the students in the MSc in Management have backgrounds that have nothing to do with business. So you don’t have to worry about that.
Of course the choice is your!
Whatever you choose, I think is going to be very good (don’t forget that both business schools are great).
If you need anything else, don’t hesitate to ask me!