I use 2 digital mixers in my setup. The advantages are: quietness, built-in effects, the ability to send 8 separate Ins into my sound card, and awesome routing options. The disadvantages are: less expensive ones may limit your sampling rate, and the more expensive ones are...more expensive, and the mic pres aren't always the greatest. If you have spent a lot of time wiring up analog gear, there's a lot to figure out, also, about digital formats and word clock and whatnot. Which leads to another advantage: now that I've converted my analog studio into digital, there is no more RF or static or hash in the audio lines, which are now S/PDIF/AES-EBU and ADAT Lightpipe formats.
For analog, you typically have to pay more to get the same quality as digital, and if you pay a LOT more, you can greatly improve your sound.
For me, it makes sense to use digital mixers w external preamps, which allows me to get good sound while sending the signal to the computer, 2 separate headphone amps, the room playback speakers, and my mixing monitors, without spending a fortune (OK, I spent a fortune, but not on the mixers).