Congratulations on getting admits from LBS and Kellogg. Both schools are finance powerhouses and send good percentage of students in private equity. Candidates attending 1yr program at Kellogg get equal opportunities as 2yr program candidates,but not having any internship creates few problems. The biggest drawback for LBS is the visa issues for working in London. Employers preferring 2Y candidates over 1Y is not very common. Do you have any preference on your job location post-mba? If not, then unless Kellogg gives you some scholarship, i would suggest you to go with LBS.