As a recent and complete convert to delta style printers. Got to say the best solution is the head moving in all three axis.
Once you're dialled in and tuned, a delta will print cleaner, faster, quieter and with considerably less of the artifacts you get in cartesian machines.
The model does not move and the way deltas move creates almost no vibrations, so you you get less detached prints (none so far) you don't have to stick things to the bed as hard as you do with a cartesian.
And you can do really improbable prints like this one:

I'm still pushing her to find the limits.