I'm both with and against @Scaz - Or maybe I just misunderstood his post.
My short version is without the 558s and the 598s in the same room you probably won't notice the difference, especially coming from a Razer headset. You'd notice they're better, no doubt there.
Similarly with and without a DAC and/or amp you likely won't notice until you have it in hand side by side.
I think its like buying a good MB/processor. Start with something affordable that you can upgrade as you get more involved in audio.
If you have the cash for the 598s, start there, if money is a concern, start with the 558s. Then add a cheap but good DAC. Then maybe an amp.
After that Scaz is right on the money - literally. Upgrading from a 598 + ok DAC/AMP combo will not see much change in performance, but it will cost a pretty penny! Not saying it isn't worth upgrading from there, it all depends on if you're really enjoying your new-found audiophile experience.
Also don't forget if you're using voice comms you'll want a good external mic! You can go cheap and get a Zalman, go mid range and get a ModMic, or go full bore and get a Blue Yeti or similar desktop mic. Depends on what you're doing (Console gaming you'd probably not want a desktop mic).