I would try them both. I feel like the game is helping me be more sensitive to stereo separation while wearing headphones as well as monitors. And (for me, anyway) my sensitivity is different with each.

Stereohead and Pan Girl are definitely harder on headphones that monitors. Train yourself on both. I started using headphones only and I have yet to beat my scores I set using my monitors.

I've been stuck at stereohead and pan girl for quite a while. I don't have a monitor setup so I can only solely rely on headphones and it''s certainly a challenge for me. But I've seen ppl leveling up using Air Pods!

I mostly use headphones, Sony 7506, Sennheiser HD 400 PRO & more recently Slate VSX

1) Increase the zoom setting in your browser so that the playing area fills to the edges of your screen.
I use 150% (per screen shot) for Pan Girl, Stereohead & Sonar Beast. Optimal value for your setup will depend resolution & size, so experiment with different values. This allows me to better visually calibrate what I’m hearing to the pan position.

2) Use practice mode (available to paid users)

I've been using a pair of Audio Technica ATX M50X headphones that are over 10 years old, they still work perfectly. I guess I should invest in a pair of monitor headphones for best results?

i use Audio Technica ATX M50X as well but not working for me. or how do i ear the frequency spectrum

It is true that higher end headphones, fed through dedicated headphone amplifier, provide much better clarity of sound and make it easier to hear small differences. When I switched from Sennheiser HD600 to Audeze LCD-XC (with a new headphone amplifier, for a good measure), my son, a piano major, was blown away by how well he can hear tiny imperfections in recording with that headset. Having said that, a pro would hear the difference with any headset. We, learners, probably can benefit somewhat from a headset with better clarity and sound resolution, but the limiting factor will still remain lack of ear training. So, the bottom line, maybe the progress will be a little bit slower with lower end headset, but it will still happen. One cannot buy/substitute ear training by investing in a headset :)