My Beyer DT880s and DT990's both sound great with the Axe FXIII also. I tried several different headphones before I found a pair that sounded great with the Axe FXIII.
The Axe FXIII is only going to sound as good as what you are playing it through. If you have bad sounding headphones or monitors they need to be replaced.
When I am going for an Eric Johnson type of sound I use my Eric Johnson Stratocaster, or some type of Stratocaster. I can not get that exact sound using for instance an Ibanez Jem like Steve Vai uses, no matter what I do.
I have found that presets made by others never sound right to me when I try them. Unless you have the exact same guitar, pickups, and studio monitors that preset was created on, you will likely have to modify the preset for it to have any chance of it sounding the same with your gear.
I also suggest building a new preset from scratch. Your choice of IR makes all the difference. The wrong choice of IR will make it impossible to get an Eric Johnson sound.