I hold an unconditional offer for both the KCL and UCL programmes in Banking and Finance.

Specifically in relation to the LLM Banking and Finance, any ideas as to which one is better?

Also, any idea as to which university is better in general?

In terms of prestige and fame, also in terms of facilities, and student life.

I am not from UK so any help is greatly appreciated!

Have a look at the ranking for UK Universities. There you get an impression of the law schools: http://www.theguardian.com/education/ng-interactive/2015/may/25/university-guide-2016-league-table-for-law