On an old LaTeX installation, things work fine, with one bug I can
correct: the URL gets broken by a % (i.e. to make LaTeX ignore the line
break) if it is a bit long, which I have to remove as it shows up in the
URL itself.=20

However, on a newer installation, the problem above doesn't occur, but
some (but not all---maybe http but not https) URLs get doubled up:
\url{\url{textofurl}}. Annoying, but can also be corrected by hand in
the .bbl.

However, on the newer installation, the URLs are not broken.

I tried using just hyperref. A suggestion to load url with the hyphens
options before hyperref leads to an options-clash error. So now I have

%\usepackage[hyphens]{url}
\PassOptionsToPackage{hyphens}{url}
\usepackage{hyperref}

Any ideas?

The problem seems to be with hyperref; just url works fine (the URL is
broken and is a real link) on the new installation as well.

But the behavious is still the same, on both the old and new systems.
My guess is that I am not the first to have this problem. If there are
no quick answers, I'll try to come up with a minimal working example.