Chromium-hardening: A repository from nepheloid

Performance

Chromium consumes a little bit more memory than Firefox, but starts up faster
Chromium tends to make better use of multicore systems, using separate processes for each tab. This feature is still in development on Firefox
The browsers have competitive Javascript performance, but Firefox has better support for the newest javascript features

Chromium generally supports the latest HTML features sooner
Firefox generally supports the latest Javascript features sooner
Both have mobile versions
Both manage bookmarks
Both have a useful dashboard startpage
Firefox is more extensible
There are countless themes and extensions, and there's an advanced Customize mode to change the placement of anything on the screen.
Firefox has an advanced user profile system that's easy to backup
Both support syncing browser data and preferences between multiple installations, including on mobile
Firefox allows non-tabbed mode, Chromium does not
Firefox allows traditional style menus, Chromium does not

There's Adblock and Flashblock for both but there exist ESR and no-addons builds for FF and Chromium
Ghostery lacks some blockage on Chromium
Chromium has a Downloadbar and limited support for Greasemonkey, Tapermonkey Userscripts by default
The Firefox extension API is far more powerful than Chromium's; every part of the browser can be customized

Chromium and Firefox are both trying to deprecate the old insecure and buggy NPAPI plugin system. Chromium uses its own PPAPI system for Flash
Firefox uses a secure Javascript-based library for reading PDFs
Firefox is developing a secure Javascript-based replacement for Flash called Shumway, but's dropped since Flash is known to be dying

Firefox uses Yahoo as its default search engine in North America, and other search engines in other regions
Chromium uses Google as its default search engine
Firefox Sync can be hosted on your own server, and uses a zero-knowledge architecture. Chrome Sync only syncs to Google servers (encrypted).
Both support private sessions where there is no history saved (private modes)

Both Firefox's and Chromium's extensions may send private/usage data to somewhere (with prior warning)
You can change the default search engines of both to services like DuckDuckGo
Users can easily disable features of Chromium that remotely use Google-services
You can selectively enable Chromium's extensions for private sessions
You can use NoScript in Firefox and µMatrix (formerly HTTP Switchboard) in Firefox and Chromium to greatly enhance your privacy
Both support the HTTPS Everywhere extension from the Electronic Frontier Foundation
Both can be configured to use TOR, but the TOR project recommends configuring Firefox or using the Firefox-based Tor browser
Firefox allows extensive control over which elements of the browser run and transmit data. These can be changed in the about:config page
Newer versions of Chromium require you download extensions from the Chrome web store or manually install from a local file