No one can really answer this question for you because it really depends on your needs and how you hunt...
Ask yourself:
Do you need the wireless headphones? No you already answered that
Do you need the extra options? IDK we don't really know what settings you are using and what else you might need. What settings are you using?
Do you need gold mode? We don't really know this either. Do you hunt for gold nuggets?
Then read this from Minelab written by Steve Herschbach:
https://www.minelab.com/treasure-talk/equinox-600-vs-equinox-800
Now how I made my choice...
I am a beach hunter 100% of the time. No difference in the 600 vs 800 for me. I use waterproof headphones so both the 600/800 headphones are worthless. I will never use gold mode - ever. I will never use park or field modes - ever. I use beach 1 and beach 2. RS is set at default. Iron bias 0. The 800 would of been a worthless upgrade for me. But for you? Go through the questions and see if you need it. Depending on how you hunt those features could be a deal breaker.
This is incorrect. The 600 keeps all of your settings.