It is not supposed to be faster (in terms of JavaScript, HTML and CSS at least), because both of them use the same engine (unless you are using different versions). However, using Chrome with a clean profile (or with certain options disabled) should be just as fast.
Chrome supports H264, AAC and MP3 which are non free codecs required in a lot of websites for playing audio and video.
Chrome has Flash built in, while Chromium does not and will not support the regular (NPAPI) Flash by the end of the year when NPAPI support is dropped (this is moot if Adobe happens to release an PPAPI version of Flash, of course, but such announcement was never made).
Chrome updates automatically with security fixes, Chromium must be updated manually or with a script that takes a build from an untrusted source (or you must build it every time, which takes hours and can be a bit complicated, unfortunately).
Chrome has synchronization, Geolocation, speech input and speech synthesis features, which I am not sure Chromium supports without an API key (and even then, it is limited to a certain amount of requests).
Crash report are not sent to Google (this is optional in Chrome, but does not exist in Chromium at all), so the crashes might not get discovered and later fixed.
There are more differences, but those were a few examples.
Also, in Chrome, you can disable most of the phone home features that Chromium does not have.
Chromium is not meant to be a browser for everyday usage, it is the open source project that powers most of Chrome. So, yes, you are advised not to use it for everyday usage.
Regarding the notification feature, I think Chromium suffers from the same feature (you call it a problem) and if you want to get rid of it, you may have to change the source code and compile your own (less tested) version of Chromium.
Frankly, I am surprised there is no way to disable it. You can suggest that as a feature, though, at
crbug.com, assuming you could not find an existing feature request over there.