In that case my two cents:
LBS would be better, although I guess the step-up is not as critical as it would be for a career-changer going full time - e.g. a scientist looking to move to Consulting/Finance
1) I would presume the average quality of your class will be higher, and so better from an experience/networking perspective
2) You may not be interested, but LBS would more likely open up doors into other consulting firms - that's where they recruit - although note that the EMBA is not really designed for this - most of the time that companies will be coming to recruit on campus, you won't be there, you will be at work
3) I have no clue about the career acceleration part when it comes to consulting - I guess if someone else pays, then why not, but would anyone ever get promoted on the strength of the MBA alone? - I would think that, more likely, it adds a little bit of differentiation on top of your actual career, shows ambition and a willingness to work extremely hard (FT job plus MBA at the same time), and may open up doors you were not aware of previously
4) I think the Exec MBA process doesn't overlap much with the other courses - which may be what you want, but also may mean that your degree of interaction with other classes and school life in general is somewhat limited. I guess that, being in London, you could maximize that part of it if you a) want to and b) make the effort
5) I am not sure it is too enjoyable to work a full-time job, to spend significant free time studying/preparing for classes, and then to spend a bunch of weekends sitting in classes - but I have never done it so what do I know...