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Yeah everyone will start about Chromium but it's not equivalent. There is no sync, PDF viewer, Flash Player implementation, print system (and print preview), auto-updater, AAC, MP3 and Opus codecs, and maybe other things I'm forgetting.You may find the Chromium project's comparison helpful: https://code.google.com/p/chromium/wiki/ChromiumBrowserVsGoo...
As a matter of fact, Chromium does support open media formats such as Opus, and (now that Google and Foxit have open-sourced PDFium) Chromium has the same PDF viewing and print preview system that Chrome has long enjoyed.
PDFium: https://code.google.com/p/pdfium/
HN discussion of PDFium: https://news.ycombinator.com/item?id=7781878
Both Chromium and Chrome allow you to sync your profile (bookmarks, extensions, etc.). The auto-updater is a difference on Windows and Mac, but not on Linux, where Chrome simply uses the same repository and package update systems other applications use.
It is true that Chromium does not, by default, come with Flash bundled or support proprietary media tags (AAC, H.264, and MP3), but the reason why that is the case should be clear.
If you do want Chrome's Flash plugin in Chromium, you only need to copy the file into your Chromium directory. There are even Linux repos that can keep it up-to-date for you.