Do you have a particular interest in Asian, Middle Eastern and/or African politics? Do you have any ideas about what you want to do after the degree?
From looking at the two courses' politics element (I can't really comment on economics), while they both offer solid foundations in areas like political theory and political research, SOAS's focus is unsurprisingly more on Africa, the Middle East and Asia, with regionally-based modules, while Queen Mary includes British politics, the EU etc. while also having a few modules that examine other parts of the world (especially in the third year).
I think both universities will give you a great education, albeit with different strengths, and you need to think about what interests you and what you can see yourself studying for three years. I can imagine the SOAS course for example would set you up well if you were interested in working in the Foreign Office, NGOs/think tanks that focus on those parts of the world, and development; the QMUL course would also enable that but with less in-depth knowledge I would think. Both courses will equip you with a range of transferable skills, and numeracy from the economics. It comes down to which course you think you'll prefer and what your interests are.
Also worth bearing in mind that QMUL and SOAS are very different. SOAS is much smaller and more specialist, but it's in the centre of London and close to other unis like UCL and Birkbeck for meeting people, while QMUL is much larger and has its own campus, so will have a different feel.