[DampRobot]

The correct answer to these types of questions, of course, is that it depends. Here's my take on it, and the thinking that got me there.

Direct drive live axle is in my mind the best way to go a majority of the time. It's best suited to a drive like a WCD, where you direct drive one of the wheels, and transmit power 1:1 between them. Live axle typically lets you cantilever the wheels, which introduces some frame design benefits and allows you to swap out wheels more easily (I'm speaking generally here). It also means that you have your bearings somewhere other than the wheel, which can allow you to decrease the size of your wheel. In my mind, a live axle system is easier to repair because the wheel and the chain or belt path isn't between two frame members.

Generally speaking, live axle drives are better when the wheels are smaller (so you don't need that extra reduction in the chain/belt from the gearbox to the wheel). Dead axles work well where you are going to have the wheel inside the frame anyway, or where you have large wheels that need that extra reduction. There's also a perception that it's "easier" to build a dead axle system, as usually it doesn't require a team to machine bearing holes themselves (they're already in the wheels).

I recognize that my beliefs are probably neither totally correct nor totally typical, and in all honesty, this type of thing really comes down to "to each their own." I'd encourage you to build/design a WCD, as it's widely considered to be a very high quality DT (generally). Most important, though, is that you consider these types of design tradeoffs yourself, and make informed decisions accordingly, even if you don't happen to end up with the type of drivetrain like I described.