In my web research I found the following general consensus (though by no means unanimous) opinion on filter types:

DE = Cleanest water, between sand and cartridge for maintenance and life cycle costs;
Sand = Easiest maintenance, cheapest over its life cycle, third of three for filtering (but still good);
Cartridge = Most maintenance (but still fairly easy), most expensive over time, between sand and DE for filtering.

All three types have their advocates and detractors (though cartridges seem to have the fewest advocates and the most detractors).

I decided to go with a sand filter filled with zeobrite for the pool we finished recently. The filtering with this setup is supposed to be nearly indistinguishable from DE but provide the ease of maintenance of a sand filter. I've been a little disappointed in the performance as I can see plenty of "stuff" in the water at night with the lights on. I suspect that this is more a function of a relatively undersized filter than of the technology as so many others are quite happy with that combination.

No matter which type you choose, over sizing the filter seems to be universally acknowledged as sound practice.