Browsers are becoming application disclosure frameworks rather than the visualization tools they were in the past. More and more services, like the Draw.io one I discussed not that long ago, are using browsers are their client side while retaining the full capabilities of end clients (such as drag and drop, file management, editing capabilities and more).
The browser I use consistently is Firefox. I do think I will move to Chromium (or at least use it more actively) sooner or later, but firefox at this point in time covers all my needs. It isn't just the browser itself though, but also the wide support in add-ons that I am relying upon. This did make me push out SELinux policies to restrict the actions that firefox can do, because it has become almost an entire operating system by itself (like ChromeOS versus Chrome/Chromium). With a few tunable settings (SELinux booleans) I can enable/disable access to system devices (such as webcams), often vulnerable plugins (flash, java), access to sensitive user information (I don't allow firefox access to regular user files, only to the downloaded content) and more.
One of the add-ons that is keeping me with Firefox for now is NoScript. Being a security-conscious guy, being able to limit the exposure of my surfing habits to advertisement companies (and others) is very important to me. The NoScript add-on does this perfectly. The add-on is very extensible (although I don't use that - just the temporary/permanent allow) and easy to work with: on a site where you notice some functionality isn't working, right-click and seek the proper domain to allow methods from. Try-out a few of them temporarily until you find the "sweet spot" and then allow those for future reference.
The abilities of a browser are endless: I have extensions that offer ePub reading capabilities, full web development capabilities (to edit/verify CSS and HTML changes), HTTPS Everywhere (to enforce SSL when the site supports it), SQLite manager, Tamper Data (to track and manipulate HTTP headers) and more. With the GoogleTalk plugins, doing video chats and such is all done through the browser.
This entire eco-system of plugins and extensions make the browser a big but powerful interface, but also an important resource to properly manage: keep it up-to-date, backup your settings (including auto-stored passwords if you enable that), verify its integrity and ensure it runs in its confined SELinux domain.