I use Chrome as my default browser, then have the IE Tab plugin decide whether the URL I click renders with Chrome or IE inside a Chrome tab.
Example: https:// my.intranetsite.com/internal needs to render in IE, but I want everything else to open in chrome. I installed the IE Tab plugin then went to configuration and added an Auto-url of "*my.intranetsite.com*". Now everytime I go to that page, or another page on that domain, it renders in IE by default, but my bookmarks remain consolidated in chrome. There's a similar plugin that will use Firefox to render the page inside chrome, so you can use chrome for all your URL triage needs. :D
(You could probably do the same thing using firefox as your master browser.)
IE Tab Plugin: https://chrome.google.com/extensions/detail/hehijbfgiekmjfkfjpbkbammjbdenadd
Firefox Tab: https://chrome.google.com/webstore/detail/icoloanbecehinobmflpeglknkplbfbm
NOTE: This solution just changes the rendering engine, so you can view and interact with sites that are normally not compatible with chrome, but you can't access things like IE's Developer Tools when in a chrome tab, or Firefox's Firebug when in a FF tab.