Hi there!
I did Korean Studies at Sheffield and I can't recommend it enough - even through covid, the teachers worked incredibly hard to make our classes as engaging and fun as possible, and they're so supportive and friendly. I've been to their houses more than once and they cooked for our whole class. <3
At Sheffield, you'll meet people who are studying all kinds of things, whereas SOAS is naturally more specialist and you won't have as much variety in what your friends are studying. Neither of these things are better than the other, it just comes down to personal preference. It's worth noting that Sheffield does have its own School of East Asian Studies (which Korean sits under), so there is specialist knowledge available and plenty of experts around.
If you're approaching things from a financial perspective, Sheffield is the clear winner! It's been voted one of the most affordable cities in the UK, and there is still plenty to do and lots to explore. Drinks are cheap, there are loads of great independent shops and restaurants, and the Peak District is a 30 min bus ride away. 🌳 It is quieter than London, obviously, but again that just comes down to your preference.
Good luck! Obviously I hope you choose Sheffield, but wherever you end up I hope you have a really great experience 🥰