Chrome comes bundled with Flash and a proprietary PDF renderer; proprietary plugins, especially Flash, have historically been a rich source of privacy and security problems.
The fully open-source build of Chrome (called Chromium) avoids that problem but is more difficult to install on some platforms.
In theory, Chrome sends your entire browsing history over to Google, since its unified omnibar doesn't distinguish between searching and typing in location. Firefox (and any browser that separates the location and search bar) doesn't have this problem.
To be frank I'm not sure how Google uses this information, but it does make me laugh when the whole Ubuntu Dash searches Amazon thing blew up. It's the same thing, really, yet nobody talks about Chrome at all.
"""Whenever you pause while typing in the address bar,
the text you've typed is sent to Google so predictions
can be retrieved. Google logs a random two percent of
these requests in order to help improve the service.
This information is anonymized within 24 hours.
"""
there is conceptionally no support for functionality akin to noscript (as in the firefox addon, not the chromium plugin with less functionality), request policy, etc. even adblock works better in firefox.
allowing these plugins is a decision that also has drawbacks. the browser will need to support synchronous callbacks (i.e. to possibly block http requests). these can block the browser, something chromium plugins cannot do (at least so easily).
Can you elaborate?