I have to take back some of what I said, above. Specifically that the CD6006 and HD-DAC1 have basically the same headphone output. It turns out that, while they are based on a similar topology and circuitry, the CD6006 has MUCH lower power capacity (about 1/12th of what the HD-DAC1 can deliver).
So, right there is a much more convincing rationale to pair the unit with an external headphone amplifier. The Graham Slee Novo will give you about 5x the power (still less than is in the HD-DAC1) the CD6006 can deliver. Other specs look a lot less convincing - I’m sure they were competitive when the Novo was new, but they’re easily eclipsed by less expensive designs, offering more power, today. If it was me, I’d skip it and buy something more current, be that Schiit, Massdrop, iFi, Monoprice - options I’ve enjoyed recently include the Magni 3, Vali 2 (reviews of both coming today/tomorrow), MCTH, LCX, Liquid Spark … and that’s all staying under $350.
On the DAC side of things … I’ve never cared for the CS4398 DAC in any implementation. I’ve heard it in everything from <$100 no-name Chinese eBay “vendor” specials to $2,500 pro/studio gear and $4,000 audiophile units and it has always left me completely cold.
I rather like the Modi 3 as a DAC (I reviewed it here)… and you have to move up a good ways in price to get something that is usefully better.
Beyond that, it’s impossible to say if you’ll notice the difference. I’d be very surprised if you didn’t, but that’s certainly not a guarantee.
More importantly, while I expect you’ll easily be able to tell the difference, it’s a lot harder to say whether you’ll like it better. Just because the end result is technically higher-fidelity and more capable, doesn’t mean that is everyone’s preference. For example, my bass-head-non-audiophile friends would hate anything that approached a neutral performance - even though it was easy to demonstrate that it is a more accurate reproduction of the source.