Well, I suppose the standalone external mixer is physically handy in that you can physically hook things up: obvious really, yet doing things "virtually" can be a bit confusing if one is starting out. It would be more beneficial if, say, you wanted to record several more folks simultaneously and have different mixes going to the individual players; If you were busy, it could be a pain going in and out of menus on the pc maybe. Any effects you used externally of course means that you put less load on your CPU...you'll also have fewer latency problems too, I'd think.
On the other hand, patching things on screen in your "card/pre" option means fewer leads: thus, you keep the signal path cleaner and you'll save money; using software effects will give you much better bang for buck in terms of quality.
Considering the extra cost of a decent standalone mixer, you'll save time and money with the breakout box option, as long as the breakout box has enough ins/outs.
Finally, seeing as something like the Emu 1616M is posh enough to have a really good bundle of sequencing software, you'd maybe spend extra in that department if you had to fork out for a separate mixer.
Think of how many instruments/players are going to be using it simultaneously too...also, if you bought a mixer, you'd still have to fork out for a guitar preamp.
I know I sound biased here..well, I confess I am really; I weighed up my options to maximise cost and quality and decided on the card/breakout option. I'm not saying this is everyone's preference or the "right" way, but it's proven logical to me. Best of wishes with this; lerrus know how you get on!