If I could give you any advice, that would be to reach out to alumni of these programmes directly via Linkedin. Also, teaching staff could be available for a chat, more likely perhaps if you meet them at an open day. The Covid period is ideal for online meetings, so you could reach out to the right people and get insight directly from them. Also, FYI most people in this forum are based in the US, rather than UK and Europe, therefore you are unlikely to get as many relevant answers.

Personally, I think that both seem like very good choices and I would be interested in knowing more about these programmes myself.

I think this is more of a question of what type of career you are looking for in the long term.  Conservation grads typically go more toward the technical route, working as consultants, in conservation studios, specialty architecture firms, etc. Architectural history/theory grads typically go the academic route, becoming professional historians or teaching.

A friend of mine did her undergrad in Edinburgh, she wasn't particularly into the mainstream architectural design for huge buildings kind of route (not sure what's the best way to phrase it) but finding out she was very into theories when she did her dissertation, and that her supervisor opened her eye on those visual/architectural theories. Based on experience, I feel Edinburgh has lecturers and tutors who are brilliant at history and theories. If you feel like you are more into theories, the intangible side, sounds like Edinburgh is your bet.

If it's more tangible, application to existing buildings - conservation sparks you more - then Bath!

Actually, I am more interested in History and want to do something in relation to that in Architecture. While I understand what professional careers you can have by doing Conservation, I am not sure about the opportunities for Architectural History and Theory graduates. I don't mind a career in teaching but I am not interested in pursuing a PhD and without one I don't think I have much chances in academics. Also since I am a registered architect from India, I am not sure what career opportunities I would have in UK after doing either of these masters. From what I understand the Conservation programme at Bath is accredited by RICS and IHBC but the Architectural History and Theory programme does not have any accreditations. So all of this is making it quite difficult to decide.