should be pretty simple honestly, ad500x is a bass recessed mids and highs forward headphone like the headphones later on down it’s line, it’s alright but doesn’t become a really good headphone till you reach ad1000x imo and ad2000x while very very good is quite expensive.
At your budget I would suggest a few, look into AKG k702 for a signature like your AD series, this does have some minor imaging issues but a much much larger soundstage and better build quality and comfort.
Better alternative would be the Tygr 300R, very large soundstage on par with akg and laser accurate imaging… this headphone has practically zero issues with fps despite having a more warm tuned signature. tygr is a redone up variant of the DT 990 and shares it’s sound placement characteristics however, it’s not a bright headphone which is why I would say 990 is slightly better in this particular regard… however it can be written off as marginal benefits
Beyerdynamic DT 770/880/990… these three are different from one another… 770 is your closed back it has a minor bass issue but works fine if you prefer isolation, 880 is a sound quality champion it does pretty much everything splendidly but could do with some better sounstage… this is a neutral bright headphone thats semi open back so no issues outside of it’s own limitations(depends entirely on the fps… if your playing smaller fps like cod or something this headphone has absolutely zero issues), 990 is the hit or miss headphone… very sharp V signature bass and treble emphasized… bass is slightly in the way but more than makes up with it due to the very large staging and incredibly good imaging topped with the treble pushing forward all fps sounds in that sound frequency, highly recommend avoiding 990 if your at all treble sensitive… Make sure if you buy an 880 or 990 to get them in their “edition” variants at 600 ohms since you have a g6 this can run them fine and you will get the best sound quality out of them this way(higher grade amps will scale with the beyers giving better sound quality).
Lastly, is just a jack of all trades which would be 58x jubilee… balanced signature. average soundstage slightly less than the ad series you have… around the same imaging, no downsides just fits pretty much anywhere except the largest of fps