As it is built on general HTML5 technologies, the application (chrome.angrybirds.com) is a simple web service and runs in any modern web browser that supports the new web technologies. However, users will need Firefox 4 or Chrome to run it in WebGL as IE9 does not support this technology and reverts to hardware accelerated Canvas 2D. Firefox 3.6 can only run the app in standard definition, while all other browsers run it in high-def.
We ran the software side by side in IE9 and Chrome and were not able to spot any differences in graphics quality or the application difference. At least from this perspective, there is no advantage gained from running the game in Chrome. the only difference is that there are Chrome-specific levels that feature Chrome logos and clouds. Down the road, that may change as the developer will offer its Might Eagle as a premium version that will be distributed via the WebStore and that will cost money. The current browser version of Angry Birds is offered free of charge.
A minor difference is the fact that Chrome can "install" Angry Birds as an app, which, however, is not much more than a shortcut from the app launcher screen in Chrome. IE or Firefox users can simply use a bookmark to achieve a similar effect.
If you're using Chrome, try Angry Birds here.