Most companies would rather not roll out and support multiple word processing software or multiple spreadsheet applications. The same holds true for browsers. Evaluate all browsers. Invite representatives from all companies to sell you on the benefits of each. Then choose one.
Doing this will give one less application for IS to support and allow you to tailor your web applications to one interface. A recent study by Zona Research among IT managers concluded that companies can save on average 20% by maintaining a single desktop browser, rather than multiple browsers.
Only one word of caution here: If you have opened your intranet to your partners and vendors (extranet), you may need to develop for both browsers, because you can't control that outside environment.