Chrome or Firefox (or browser-agnostic) for an intranet app?

Go browser agnostic. There's no telling when somebody will mandate a certain browser, and you'll be stuck having to redo a certain module because it used a special plug or feature only available with the browser now outdated.

Technically we're an IE shop here, but I make sure all my apps function on at least IE and Firefox, and I'm doing more testing in Chrome as well.

What is the business' IT policy on browsers? It seems like this would determine what you write it for. Why write it for either, if every computer at your client's company has IE6? Lock-in is not a problem for a company as they can dictate the policy on what people use and must have on their computers.

Speedwise you're not going to find significant gains choosing one over the other unless you're doing specific tasks that play towards their strengths (look at the range in benchmarking for instance, some google tests have chrome hundreds of times faster, where as others have firefox beating chrome).

Ideally, you'd want it to be agnostic, but if you had to choose one though, I would go with Firefox, as it's a more mature browser. I'd be reluctant to target the app for a browser that is only a couple months old, especially one that just hit 1.0.

Although being standards compliant is certainly have many advantages, if your application is UI heavy and you don't want to struggle with lack HTML widgets, I suggest using a Gecko based browser which you can build UI in XUL much quicker with all the familiar functionality of a desktop application than HTML from scratch. Since Gecko is open source and actively developed, you don't risk being stuck if you were using something proprietary.