Not only are light meters more versatile, you can do a few kinds of metering with them that you can't with cameras (and vice versa).
The meter you've linked (and I happen to own) has two kinds of metering: reflective and incident. Also, light meters can meter for flashes/strobes, something you can't do with modern DSLRs.
Reflective metering in the metering you know from DSLRs; light is reflected off your subject and back into the camera. While this kind of metering has many advantages: you can meter from far away, you take into account the whole scene, etc., it has many pitfalls. A scene with lots of snow or a dark wall can fool it. I'm sure you have a some images that are poorly exposed for no reason, among a series of well exposed images - that's what happens when a reflective meter is fooled.
Incident metering is a bit different; it allows you to measure the light falling onto a subject at the point of that subject. That gives you a "truer" exposure, one where dark material will come out dark and light material will come out white. Sekonic has a pretty good FAQ entry on the subject. When shooting people, you would measure at the subject's face with the dome pointing at your lens, something you often see in movies.
With a modern flash meter, you can also meter flashes and strobes. The meter you linked can either be hooked up to a PC sync cable, or can be set to react to a flash of light. This lets you measure the results of strobes you've set up without using a digital camera or a polaroid. It also lets you check that you have nailed your exposure, without checking your LCD a thousand times.
In addition to measuring the whole scene, with incident metering, you can measure the light from each of your strobes, and if you ever look at strobe notations, that's how they're usually recorded. This you measure at the subject, pointing the white dome at your various lights while firing them off separately. This lets you quickly jot down your flash ratios, and that's extremely useful when recreating a look.
Oh, and the reason I often carry that Sekonic meter around: It's much, much smaller than my DSLR and I use it for my film cameras that don't meter.