First off, congratulations on being accepted to both universities. I am relieved I found your question because I am actually in the same boat as you. I received an offer from both LSE and Oxford (within the social sciences and policy department) and tried to see what folks did before. But one thing that my current professor told me is that if you want to go into the public sector/ politics go to Oxford but if you want to be an academic or in a more specialized field within the finance sector go for LSE.
I am from the United States and back home Oxford has a more prestigious name recognition so that’s one metric I’m using to decide. How is it in your country? I also recommend finding people on LinkedIn that have taken your program, I connected with like over ten folks that were all happy to help.
One thing to say about LSE that I heard from a current master’s student is that strike action severely hindered his term for in-person classes. That is a huge con for me and a plus for Oxford (And at the recent LSE orientation for offer holders they could not guarantee if classes would be in person). Also, it's worth looking at the student satisfaction rate because Oxford routinely beats LSE. Furthermore, Oxford beats LSE for the quality of education.
Living in London currently, one thing that I do appreciate about LSE is that it's in the city center of London and that it is not removed from the populous.
On the financing part, it really depends on your career aspirations, doing a cost/benefit analysis if you think you would be able to pay it off in the long term then I say it is alright to invest in yourself now.