CS4398-CZZ is the DAC and JRC 2114 is the dedicated headphone AMP in SoundBlaster Z, which also had a JRC 4556A speaker amp in which people sometimes prefer to plug their cans.
I’m basically trying to nail down where my PC’s soundcard stands compared to normal amps and DACs, for the purposes of determining what headphones it can drive.
Thank you. 
Sorry, that’s the op-amp. The headphone amp is MAX97220A.
I use a Micromega Mydac that uses the CS4398. It easily outperformance my schiit Modi 2 uber, Modi 3, and bests my Dragonfly Red, but not by as big a margin.
The issue is the mydac uses it’s own switching power supply and a very smartly laid out PCB, wima caps and good quality oscillators so I’m guessing this is a non standard implementation.
What I’m getting at is, the DAC chip itself cannot be used as a benchmark for the performance of your sound card. A better question would be how does the SoundBlaster Z compare to modern dedicated entry level dac/amp.
Any guess?
At TechPowerUp I found this piece of information:
So it should run those 600ohm headphones, but like you say, the real question is, is it good enough to use, or should it be replaced as a priority.
If it sounds like the soundblaster cards I had nearly 2 decades ago, a Modi would be a good step up. But it’s really impossible to tell. You should just get a cheap ~$100 dac from Amazon with a return policy and compare yourself.
Used is a good option too as you could buy/sell at minimal cost to you if you don’t like it.