Pros & Cons of Buying an Integrated with Built-in DAC?

There is more to DAC performance than what chip is used.  I have the Oppo 105 Universal Player/DAC and the freestanding DAC Mytek Manhatten. Which uses the same chip.  The comparison isn't close; there is so much more detail with the Mytek.  Of course the Mytekhas a much bigger power supply, and doesn't have to divide it 's power to a multiplicity of tasks, like the Oppo.  I will be suspicious of Integrateds with included DACs for that reason.  I would by a separate entry level DAC and a traditional Integrated Amp and then upgrade as needed

You sound pretty happy with your present set up, so why the desire to change?  I am guessing that for under 1K for a new DAC you will be making a lateral move. Not to disparage any DAC in that price range, but Hegel has a solid reputation and I suspect that the DAC  in your integrated would probably be comparable to others in that range.  Keep in my mind that I haven’t heard the Hegel, so I could be talking out of my a**...
  At 2K you are into some seriously good DACs by Mytek, Benchmark, Schiit and others.
  Of course you could get a used DAC, as you did with your amp