From my experience the 783 has a smoother action and better trigger than the Axis. The 783 plastic stock has more flex than the Axis. The Axis and 783 both have chassis and barrel options.
Trigger depends on Axis or Axis II. The II with the accutrigger is a better comparison to the 783 price-wise, and the triggers on those are on par with the 783. It used to be the case that you could get a rifle basix trigger for the Axis for the same as the price increase to the Axis II, that's probably not the case anymore though.
Both suck compared to my Rem700 factory trigger.