Hi! Of course—I'm happy to help in any way I can. Two things to bear in mind: I was at Birmingham for much longer than Warwick, and I did a taught degree at Brum and a research degree at Warwick. For those reasons, I can't compare them 1:1. But I'll do my best to answer your questions thoroughly!
(1) In terms of career prospects, Warwick probably has a very slight edge because of its reputation—in general, it's considered a little more prestigious than Brum (though whether/the extent to which that applies very much depends on the field you want to go into). I got a decently paid job shortly after finishing my master's, and it was the skills I'd acquired rather than the institution(s) I'd attended that got me the job.
(2) It's difficult for me to properly compare the teaching because my master's was a research degree, but I did sit in on some of the taught lectures at Warwick. The quality of the teaching is, in my experience, very similar—it's top-tier and delivered by knowledgeable, passionate lecturers who really care about their subject and their students. I preferred the teaching at Birmingham (albeit by a very small margin) because I liked the way the lectures and seminars were set out—the seminar groups were very small, which made it easier to revisit lecture material I didn't understand. I don't know what the seminar group sizes are like for undergrad modules at Warwick, so it might be worth asking about that at an open day if it's something that matters to you.
(3) The lecturers are very approachable at both institutions, and I had really good relationships with the staff at both places. For me, Birmingham has a slight edge in terms of feedback—the lecturers who taught me there gave incredibly detailed, specific feedback that enabled me to improve the quality of my philosophical argumentation and writing very quickly. I was also given a document that clearly outlined a suggested essay structure, writing style, and tips and tricks, which was super helpful when I was first starting out. I received very helpful feedback at Warwick, too—again, it was detailed and specific. For reference, I achieved similar marks at both Brum and Warwick, so I think the quality each institution expects of its students is pretty similar.
(4) Birmingham has something called the Birmingham Award, which is an employability programme for undergrads. I completed the programme and found it useful, and it looks good on a CV. Warwick has a similar programme (called the Warwick Award). I also did casual work as a student fundraiser at both unis (phoning alumni to ask if they'd consider donating to various schemes), which was probably the most useful thing I did in terms of career prep besides earning the right to say that I have a degree. I don't feel that one uni did a better job than the other of preparing me for the world of work.
(5) I enjoyed my time at Birmingham more for non-academic reasons—I met and moved in with my best friend there, and I like Brum (the city) a lot more than Coventry. I also have a soft spot for Brum's campus—the architecture is beautiful, there are lots of green spaces, and the library is excellent. So while I don't have a favourite academically, Brum is my overall favourite for the reasons I mentioned.
(6) Before I started at Birmingham (and university in general), I wish I'd known how important (and encouraged!) it is to make use of lecturers' office hours. I'd also recommend thinking about the areas of philosophy you're most interested in and looking closely at the modules on offer—and the research interests of the lecturers—at each institution. I'd advise you to make your final decision based primarily on which department has modules that best suit your interests.
Honestly, I think you're in a great position. Both universities are excellent and have outstanding philosophy departments. If you have any other questions, please let me know. Good luck!