Until recently we have been using SVN for all projects of our web studio, and there is a very convenient feature present in several clients like Subversive and TortoiseSVN that
Building on Jerome's answer this will get you the copies of the files that changed in revision 4:
hg archive --type files --rev 4 -I $(hg log -r 4 --template {files} | sed 's/ / -I /g') ~/changedfiles
That puts all the files that changed into revision four into a newly created directory named changedfiles in your homedir.
If you change it to:
hg archive --type zip --rev 4 -I $(hg log -r 4 --template {files} | sed 's/ / -I /g') ~/changedfiles.zip
then they show up in a zip archive.
It's worth noting that that only works if you have no spaces in filenames. If you made that blunder then we'll need to use hg status --print0 -r revision -r parent-of-revision
instead, but hopefully that's not necessary.
Note also that the revision number, '4' in our example, shows up twice. The whole thing could very easily be wrapped in a shell script, and that would be parameterized so you don't have to remember to change it in both places.