Hi,
I'm an Oxford alum so I can help with some of the points you made and offer some extra info.
Sandro1994
I very much enjoy consulting and I can see myself staying in consulting for ~3-5 years after the MBA. I have a particular interest in the blockchain space and I thus might found a startup or join a tech company after that.
Oxford Said established Oxford Foundry and they do a lot of work with university and some external startups. They also offer Blockchain courses for free to students as well as entrepreneurship courses in the evenings. Also, an entrepreneurship project is part of the core MBA curriculum at Oxford so there's a chance to pitch a real project to a group of VCs; it's great experience. (Maybe Yale offers the same?) There's also the chance to get involved with helping startups as an MBA student at Oxford Foundry, which was one of the best parts of the MBA for me. It's not a formal part of the course though so students have to take responsibility for finding an opportunity.
Also, a lot of consulting companies visit Oxford (in case you want to jump ship to another employer). There's a list in my post history of consultants that visited us. Oxford isn't far from London by train so I was able to attend consulting events there as well.
If there's any chance that you won't stay in consulting, know that it's quite difficult to recruit internationally so you'd have to accept that you might finish the MBA with nothing lined up until you can get to your target country (not a big deal honestly).
Sandro1994
I would enjoy the many electives and the possibility to take courses from the wider Yale university.
Oxford had LOADS of great electives and one of my biggest regrets was that I didn't have the opportunity to take all the electives I wanted to because of the 1-year format. I knew going into it that would be the case but I could only commit to a 1-year MBA due to being self-funded. Given your employer sponsorship your priorities will be different and being able to take more courses would be cool. You can audit other electives but the timetabling is likely to clash and the workload is high enough without adding in extra electives for fun.
Sandro1994
The business school does not have a good reputation within the broader Oxford University
I hadn't heard that. I don't know if this is something from when the school was new or maybe a student's perception? In any case, a minority of the non-MBA and non-business school students had a bit of an attitude when I interacted with them at college events but most MBA students are older than them and we're paying more than 5x their tuition fees so we get fancy things.
I don't know if any of that has helped or if I've muddied the water further!