I don't think the analog circuitry is active at all in the DAC2-HGC when it's not the current input (you hear relays clicking inside the box when you select it) so there shouldn't be any better noise handling with the DAC2-D.
Benchmark themselves aren't making any claims about reduced noise or otherwise improved performance.
Personally, even if I was not intending on using the analog section now, I would still buy the DAC2-HGC instead.
$200 does not seem like nearly enough when you consider the flexibility you are giving up.
Even if you might not be using it now who knows what your audio setup may be in a few years time.
With the analog stage of the HGC, you can run any other audio equipment through it and make use of the excellent headphone amplifier, or the remote controlled volume.
For me, the DAC2-HGC is a long-term purchase. I am so pleased with its performance that I can't imagine wanting to replace it with another DAC or headphone amplifier. It just seems short-sighted to forego the analog input stage and 12V trigger to save 10%. But maybe if you're really sure that you will never use them, that will be a worthwhile saving to you.
Something else to consider is that if you ever do intend to sell it on, potential buyers may not want one without the analog inputs.