Sounds great... But what is the "Google agent"?

The Google agent is an option, enabled by default, to send (anonymous?) usage statistics to Google such as installs and country info etc back to Google; no option to disable it as far as I know!

If you mean permission to access your account as a means to improving service that's presented when you first open Chrome after downloading, it's true that you won't find that on Chromium. But that won't stop Google from tracking you on Chromium in order to report your data to its clients. Even if you use the Ghostery and Opt Out of Google Analytics apps to block tracking they won't work every time in either browser.
If you want to stop Google tracking what you need to do is go to Google Dashboard https://www.google.com/dashboard/ and sign in to Google there. Look closely through your initial options and you will find an option to "pause" Google tracking which you should choose, and another option to erase Google's record of your history which you should also choose. Google will stay "paused" indefinitely unless you come back to Google Dashboard and end the "pause" manually.
If you want to be thorough you can continue looking through the other items in Google Dashboard and erase the permissions to access that you have given Google over the years. Unless Google changes its privacy policy sometime in the future you will be opted out of Google tracking indefinitely. If you doubt that you can always go back to Google Dashboard and check for yourself. This will be far more effective than any naive belief that you won't be tracked by Google if you use Chromium instead of Chrome. They have identical GUI's and both will track you unless you use Google's Dashboard to opt out of it.
Of course literally hundreds of other tracking services will continue to follow you on all browsers using "bugs" and cookies. Use Ghostery in the Chrome/Chromium app store to attack this problem and the "Cookie" app by Sweet Productions, which can be found on MU, as a backup

It's not just usage and tracking your activities online that makes chromium more appealing than chrome. I do not know much about it but I remember when I first installed chrome a long time ago it would randomly be connecting to the net in the background, would download updates without permission, and just other automatic features that were not appreciated. If you google, the irony, you will find out lots about how to use chrome and stop many of these auto-features that users don't like. If I remember google created a launch agent named keystone or something similar, so you had "google" running at launch every time you started your computer, sending info back to google and downloading updates and who knows what else. It is possible to deny read/write access to the folder I recall which stops many of the issues but all of this is old as I have not used chrome in a long time and I am sure some things have changed. Chromium is the same browser and many of the chrome extensions work just fine on chromium so if your worried about google but like chrome, stick with chromium or do a search and learn more about the "nefarious" features of chrome that many users do not like and how they can be remedied, which they can.

well, in this version there is an update agent, at least with me (chromium - check for updates

The Google Software Update Agent is a background service that automatically updates Chrome. In this version of Chromium, there is a menu option that checks for updates (as it is said in the FreeSMUG website, they've added Sparkle framework to check for updates) but it's not an agent/service.

Anyway, guess it's the only relevant difference...

Chromium doesn't track you and gather information about you like Chrome does.

They even have the same numbering? What gives? Why, why, why?

Would you mind giving us some details why you hate Chromium so much?

I think you are talking about your own taste, not about the browser as such - to me Chromium is a great add on and I am using it parallel to Safari.
Please consider your rating in an objective way, this post does not help other users.

thanks

SRW Iron is certainly ugly garbage but what;'s wrong with SMUG Chromium? And which browser on the current market is "pro-culture" and "pro-art"? I'd like to try it.

David here likes to word, "rubbish," quite a bit. Read his comments for TenFourFox. Chromium has a nice UI, IMO. To each his own, but it's streamlined and simple and that's one of the reasons so many people are using it, as well as the features and speed. I like the tabs implementation and if you don't happen to like the theme, which I do, you can choose from numerous other themes. So don't take David's advice. Spend time evaluating software for yourself and take all reviews, including mine, with a grain of salt. In the end, you have a choice, so try it out for yourself and use what YOU like.

Don't worry about it. From personal experience I know that you'll receive the same message every time you launch Chromium under the circumstances you describe, but your profile will work anyway despite the warning.