Hi!
I am also thinking about applying to LSE Management & Strategy.
I think the main difference between the two is that the Msc in Management from UCL is a masters degree in general management, with a focus on finance topics, while the LSEs Management & Strategy is a degree in applied economics: At UCL, you will be doing different topics in finance and general management, while at LSE you would be doing a lot of applied game theory. Additionally, LSE has a reputation for being very research-focused in their teaching. If you do not enjoy reading and discussing papers, I would not recommend LSE. Most other Management schools in Europe have a focus on applied teaching. I am not sure about UCL though. Also note that UCL includes one elective while LSE allows three electives.
Reputation-wise, both are top-notch universities. However, Management-wise I perceive LSE as having a better reputation. UCL is not really famous for management. LSE has a very strong employer reputation in London and Europe in the fields of consulting and investment banking with all top firms recruiting on campus. I don't know about UCL - I think it is more famous for arts humanities, psychology and traditional science subjects. However, as it is one of the best universities in the world, UCL will not close any doors for you.
Have you been admitted to both? In that case, I would decide by the programm structure (general management with a finance focus at UCL vs applied Microeconomics and electives at LSE), and your post-grad goals: If you want to go into consulting or IB, choose LSE, otherwise, both are good schools.