which uni is better?

I would say LSE, not that I am biased because of my offer for Management but according to league tables, LSE is always above UCL in Business Management:

http://www.theguardian.com/education/ng-interactive/2015/may/25/university-guide-2016-league-table-for-business-management-marketing
http://www.topuniversities.com/university-rankings/university-subject-rankings/2015/business-management-studies#sorting=rank+region=+country=+faculty=+stars=false+search=
http://www.thecompleteuniversityguide.co.uk/league-tables/rankings?s=Business%20%26%20Management%20Studies

I would not say that you should definitely trust those league tables, but these give you an idea of reputation. However, think it worths a visit to both, or contact with as many current students as possbile and find out which one you would prefer. And good luck!

Just for the record, LSE's course is BSc in Management, not Business Management, and there is a difference because management is applicable not only to business but also for public entities and not-for-profit NGOs. UCL's a Management Science degree.