First off, congratulations on the offers, I've received an offer from LSE but I'm still waiting back to hear from Cambridge.
Honestly, even if I got into Cambridge, I would still probably go to LSE. From searching the forums I haven't heard anyone say anything positive about the course in Cambridge which is slightly worrying. I've heard a lot of people say that the MiM at Cambridge is always seen as second best when compared to the MBA programme.
I think either way your career prospects will be pretty good especially with a year of experience under your belt. You may not get into MBB but there are plenty of other consulting firms out there. Both universities are well regarded all across Europe so I don't think choosing either one of them will hurt in terms of prestige.
Again, this is all second hand information, but this is what I've generally heard across this, and other forums.
In terms of rankings, LSE's one year course is new so it's not ranked on FT. I read somewhere that Cambridge isn't participating in the FT rankings because Cambridge doesn't allow external internships and that's a criteria used for rankings.
Let me know if I can be of any help and good luck!