Well from a technical standpoint digital input should be better. A pure digital signal is, in theory, always better than a digital signal concerted to analog and converted back to digital.
The sony has a good scaler, it may or may not be better than the one in the ax100. If it is, then it is better to upscale using the DVD player rather than the projector.
I would make sure you read about the sony on the DVD forums as there are many valuable insights on this dvd player and how to set it up right.