It's easy to see how much relief there is in the neck, especially with a zero fret. On a "normal" guitar, you capo the first fret and then press down anywhere from the 14th to the 17th fret. The distance between the string and the frets at the 7th to 9th fret is the relief. With a zero-fret guitar, the procedure is the same, but without the capo.
Too much relief can lead to excessively low action starting anywhere above the 10th fret, or excessively high action starting anywhere below the 14th fret. Too little relief can lead to buzzing low on the neck, particularly below the 7th fret or so. The less relief, the more accurate the intonation. String weight has lot to do with how much relief is desirable. Bigger strings, up to a point, vibrate more and have more of a tendency to buzz against the frets, but REALLY big strings are tighter and don't seem to buzz as much.
The best intonation comes from large strings, low action and as little relief as possible, even to the point of having none at all. The best sound (intonation considerations aside) comes from large strings and higher action. More relief can eliminate buzzing, but a guitar will be louder and more resonant with less relief, since relief lessens neck tension and decreases the transfer of vibration from the neck to the body.
Overall, I'd say it's best to keep relief to an absolute minimum and solve buzzing issues by raising the action or dressing the frets. On the other hand, if everything else is fine but notes and chords on the base position or slightly above it sound a little sitar-ish, it's probably best to introduce some relief and compensate by lowering the bridge slightly.