With the release of umbraco v4 Release Candidate many changes have been made to improve performances of the back-end in all the browsers. Right now, personally, Chrome appears to work great. If I experience bugs, inconsistencies, or oddities with umbraco and a particular browser, I'll note it here.
Weeks later. . .I've been using Chrome to work with umbraco, and it is awesome. Everything I've tried to do has worked, and I only use IE for checking rendering. Firefox is useful for Xml and Web Dev Toolbars, and FireFTP.
Starting with version 4 the domain of the umbraco installation under question, when working with the site back-end, is included in the title of the page. This facilitates having a local site for testing and a remote site for deployment, and keeping windows or browsers straight, or for whatever reason you may have multiple sites open.
The default means of accessing the umbraco GUI, last I checked, though, displays a tool window that doesn't allow other tabs, or even editing the url. That is what happens when you browse to, for example, "localhost/umbraco" and the Default.aspx is shown. If you instead browse directly to "localhost/umbraco/umbraco.aspx", the GUI will appear in a normal browser window or tab.
