Good headphones for the Korg SV1?

[MangoT]

Hello you all sensible ears,

I recently purchased a Korg SV1 88 Black edition with keyboard amp/PA system: Behringer K900FX. I definitely noticed that the sound is better plugging headphones directly through the Korg (my Audio-Technica ATH-ANC9). I knew it before buying it anyway.

Now, I bought the ATH-ANC9 a couple months ago for different purposes: travel, study, basically for quiet moments and I'm happy with it (it has the noise cancelling option). However now that I purchased the Korg SV1, I am wondering if its not better to get a better headphones for this kind of us.
The cable on the ATH-ANC9 is a little too short in my opinion, and since it runs on one AAA battery, I will use too many batteries while practicing with this headphone. So I'm considering buying new headphones more appropriate for amp/monitor or to directly plug in the SV1.
My question are: what headphones are you using with your SV1? Do you know if it will be better than the ATH-ANC9? Are there any headphones specifications that I need to look for, for using withe SV1?

Thank you

Thank you!