Regarding a bigger name, I find it hard to believe that *in the chosen field,* Leiden is more prestigious than SOAS. The latter was ranked #6 in the WORLD this year. I know several alumni from their development program, and they told me that potential employers have commented positively on the fact that they attended SOAS.
That being said, obviously there's a lot more to consider than rankings and name. SOAS is a specialty university: if you have a regional interest in Africa, Asia, or the Middle East, SOAS is the place to go. Plus, London will give you more opportunities for networking and internships. Look at the curriculum of each program and identify which courses you'd want to take and what skills you would get out of them. Get onto LinkedIn and see where alumni have ended up. Consider how connected the faculty are, and whether they have mostly academic or practitioner backgrounds (one SOAS Dev Studies alumnus told me that faculty were very happy to use their connections to help the students network). Good luck with whichever you choose!