innuos pulse compared to denafrips gaia 12th

I'd easily choose the Pulse over Gaia with computer as streamer. Next to the dac, streamer is most important streaming component. Using a general purpose computer as streamer means high levels of self generated noise, poor clocking, and once you've lost here nothing post streamer can restore whats been lost, it also defeats the whole purpose of a DDC in that optimization of INPUT to any DDC is also critically important.  Inserting a high end DDC is only worthwhile if one already has nice streamer, optimized input (most likely usb) into that DDC and DAC with I2S input.

@sns What good streamers come with I2s?

If you insist on I2S output not too many, most will use usb out of their streamer into a DDC in order to use I2S, this what you'd do with Pulse. As for streamers with I2S just off the top of my head Holo Red is reportedly very nice.

I would recommend using USB from any streamer into a Denafrips DAC. These DACs reclock the input data. If you use a synchronous input (anything other than USB), you risk FIFO overflow or underflow which will cause audible glitches.
 

I currently own the Terminator Plus and owned a Terminator previously. 
 

I’d recommend focusing first on getting a good USB streamer, and then if you have a Denafrips DAC with clock outputs, you can consider a DDC such as the Gaia.  If your DAC doesn’t have clock outputs, I think you are better off skipping the DDC and using USB directly into the DAC.