My personal experience:
They are almost exactly the same, on average. I had been using WinRAR (almost)exclusively because of its “Password Protect File Names” feature, but 7zip does that now, too. Didn’t last time I tried it (or I was smoking a huge bag of crack and missed that, I don’t know.)
For example: 7zip does a better job overall, but WinRAR does better at compressing files already compressed by another algorithm. Compressing a folder full of anything but JPGS, MP3s or Packaged EXEs = 7zip wins. Other way around, WinRAR wins… usually.
(For the Geeks: I use the highest compression setting possible, with the solid archive option)
As I have done many times in the past, so I do now: going through my billions of archives, extracting them then recompressing them with a new program to see which one compresses better.
The weirdest thing of all: I have 3 or 4 archives that ALWAYS compress better with WinZIP, by a large margin. Yeah, I don’t get that either.