Edinburgh's reputation

For what subject?
In general yes it is prestigous and well-known and relatively hard to get into.
In comparison to Aberdeen I'd say overall it is better. I'd say relatively similar to Glasgow (potentially higher if anything) and I'd say St.Andrews is the best. But this will vary from subject to subject

Thank you for your opinion. I was only asking in general, no specific subject

Reason I was asking because the subject can make quite a big difference

Thank you for your opinion. I was only asking in general, no specific subject

There is a difference in teaching quality for a specific subject across these university. I.e Edinburgh does not fair well in engineering compared to Glasgow but it does well in literature, medicine and informatics, etc.

Reason I was asking because the subject can make quite a big difference

Thank you for your answer. Would you say that Edinburgh does well in Computer Science/ Data Science?

If you Google "best unis in the world for AI" you'll usually find Edinburgh there. No other Scottish unis make it to the lists.

Y
Yes, I will say so. The curriculum prepares the student well by building a strong foundation in the beginning.
You can have a look of the curriculum here.
http://www.drps.ed.ac.uk/18_19_Archive_at_01-09-2018/dpt/utcmpsi.htm

I cannot find much information of the other universities, but if you do, I would suggest you to benchmark it with Carnegie Mellon School of Computer Science. They are one of the best school for computer science program.
https://csd.cs.cmu.edu/academic/undergraduate/bachelors-curriculum-admitted-2018

If you ask such a question in the UofE subforum you are obviously going to receive a big number of biased feedbacks...
Anyway, to answer your questions:

Would you say that Edinburgh does well in Computer Science/ Data Science?
I would probably say it's one of the best universities in the UK for this subject.

Is it considered a prestigious (a), well-known (b), and hard-to-get-into (c) university?
(a) and (b) are much relative to your own definition of the terms used. UofE is well known as much as any other top 10 university in the UK, but it's surely not in the same league as MIT, Stanford, Harvard, Oxbridge, etc. I would say it's much closer to Bristol, Manchester and other such universities.
(c) mostly depends on your fee status. Sad but true. It's quite easy to get in as an international student, less so as RUK, and extremely hard as an EU one. To make a 'practical' example, I know of international and RUK students doing a fy course who managed to get an offer with 70%, whereas I got rejected having achieved a 90% and being told that despite my high results 'I didn't meet the right entry qualifications'. Note that a 20% difference is no joke.

How does it compare with the Universities of St Andrews, Glasgow, and Aberdeen?
I would say it's comparable to St Andrews and better than both Glasgow and Aberdeen. St Andrews might offer better teaching standards though since the university is much smaller.