I am familiar with LSE and Sciences Po MA HRHA, albeit not with UCL.
It depends on your areas of interests and professional goals. The syllabi btw LSE and PSIA are different. At LSE you choose your concentrations, essays and dissertation. 1 yr format. Have you made effort to look at individual modules: reading list, teaching methods, learning outcome and exam? i thought it was clear from correspondence with people with admissions at both unis.
PSIA: Broader, more modules but not as in depth. thematic and regional concentrations, electives in language and professional development. Exams in Dec, May and mid term assignments. The workload is formidable. note: 2 yr format with 3rd semester either dissertation, exchange abroad or most popular internship at gov or NGOs. Though tougher for international students to find jobs. Some adjuncts come from the field and bring in practical perspective (ie CEO of doctors without borders teaches a popular module). PSIA may offer in some aspects a better regional concentration in Middle East or Africa than LSE. Overall review varies from average teaching to excellent, depends on prof. PSIA has an odd registration for modules, first come basis. Some students can't get into popular modules. Some complaints about cramped library. If you are fluent in French, you can participate in more activities.