The big differences seems to be in the way they do their thing: I'm reasonably sure homebrew just git clones then updates the local repository normally[0], it has "only" 2500 files in Library/Formula, and because of its different subject it is way less write-active, CocoaPod has 1k commits/week which look to be increasing pretty much constantly, homebrew is around 350 with ups and downs.
Also not sure it matters, but homebrew has lots of commits updating existing formula, cocoapod changes are almost solely addition (publishing a new version of a package adds a new spec and doesn't touch the old one)
[0] which is exactly the bread and butter of github