Newbie here. I see that most of the guys have separate monitors AND headphones. Why not just use one thing?
Headphones: The advantage here is obvious - loud as the player wants without disturbing others. Headphones have disadvantages though - like no controllable feedback for instance.
Powered monitors or power amp & guitar cab: Sometimes you just gotta move some air.
Sometimes out of necessity (gigging, rehearsal, jam session, etc) and sometimes just for the sheer joy of it.
Having both options is always nice, even if unnecessary. Budget may dictate a user's options. For the home user on a budget and with no 'need' for a loud monitoring system headphones are where the bang for your buck performance may be found. A $200 pair of Beyerdynamic DT-250 80 ohm headphones will be far more accurate (and thus likely more enjoyable to hear oneself play through) than any powered monitor solution anywhere near this price point. I was $450 into a pair of nearfield studio monitors (Equator D5's) before I even approached the audible performance of the DT-250 headphones, and $1,600 into powered monitors (Atomic CLR powered wedges) to surpass the performance of the DT-250's.
I have other headphones as well, including the well-regarded Beyerdynamic DT-880 Pro's (also very enjoyable to use with the AxeFX II) as well as standalone headphone amps and a dedicated DAC. For use with the AxeFX II I prefer accurate representation of its output over a hyped sound - most of the time - and the DT-250's are at an excellent price/performance point for this purpose. I believe one would have to spend well more than three times the DT-250's asking price to find any significant performance gains in accuracy.
Likewise one would most likely be looking at more than twice the now $500 price of the Equator D5 Studio monitors for any performance gains.
I don't believe there is a more accurate playback solution than the powered Atomic CLR monitors available anywhere near their price point. I put my money into the CLR's because I have other uses for them besides blowing the windows out of my house playing guitar (they are currently my favorite music playback system of any I've owned or spent time using, and by a very wide margin.
Some headphones were already here when I bought my AxeFX, some followed later (I like headphones quite a lot). The AxeFX pretty well drove the upgrade in studio monitors and the purchase of the Atomic CLR's. The sale of tube amps for which I no longer had a use helped pay for the new monitors and CLR's.
As always YMMV and IMHO, of course.
