I've been around both, and both work really well. In one of my articles about Haiti I discussed the options.
Each situation is different, so what might work at one place might not at another. The biodigester can be simple to set up, but still requires space. But you can use a simple 5 gal bucket with the composting method, as long as you have ready access to some sort of duff (sawdust, moss, shredded paper/cardboard, etc). As long as it's covered, it won't stink. Generally, about a 2/3 duff to 1/3 humanure ratio works pretty well. Urine can go straight into the garden. It's great stuff. Just move it around, and water it down if possible. Some folks have toilets designed to separate the two, but I've not tried my aim in one. :P 
We're in town, so have to be careful we don't get caught doing certain things. So far, we haven't solved the manure side. I want to build a shop with a bathroom designed specifically for this, without looking like it is. I think the local regulators would be unhappy and impose some form of onerous extortion upon us if they found out.

I just remembered another aerobic system I saw that worked well too. It's a wet system that uses a regular flush toilet, but it does have to be elevated at least a couple feet. A lot of houses are elevated anyway, so it's no biggie. But for those of us with concrete foundations, this might not work (unless you want to elevate your throne!).
The toilet flushes into a large enclosed bin outside where it pours over rocks. At the bottom is a pipe system that allows the liquids to escape into what's really just a greywater purification system. It's a sealed planter with large rocks at the bottom, gravel and then a membrane to keep the topsoil from getting into the bottom. There are different ways to do it, but you just plant reeds and grasses in it, to help clean the water. Then it leeches out into another planter where you might plant flowers or whatever, but probably not edibles (just in case). The water going into it would be good, but it's a precaution most take... plus there's the liability factor.
The bin is full of rocks and topped off with logs and wood chips. A bunch of red wrigglers are added to the mix, along with some fruit and other compostables to give them something to eat. The humanure gets caught in the chips and stuff, then the worms will start eating it all up. Eventually it liquefies enough to get through and go through the pipes. 
The folks who made it said that it got pretty stinky after the first week, and past two weeks, but then it started balancing out and the stench went away. Now it doesn't stink at all, except maybe when you're opening it up. It has it's own microsystem that maintains itself with the constant input. And you can throw your compost in this as well, if you want.
There's a nice video of this one online, but I can't recall where. Sorry. :(