I am not entirely sure but I do have the impression that LSE isn't well placed for Psychology in London, and KCL / UCL are renowned in the field. Leaving rankings completely aside, LSE's program is different because of the behavioural sciences modules. It is a BPS-accredited course which means it has the same core modules requirements like KCL, UCL and all other BPS-accredited courses, and the difference is the elective modules where you will cover studies related to public policy, economics and society at large. Presumably you have looked at what these modules are since you have mentioned that you prefer the course to KCL's. I personally feel that the placement at KCL trumps LSE's course BUT this is because of my intention to pursue clinical psychology, and I require supervised work placement. So I guess, it depends on what you really want to do after university, and this may help you decide which course to pick.