I own both an AxeFx and a KPA (powered toaster version)
I do quiet practice at home - I prefer total quiet practice - so I use headphones
I also like to play along with backing tracks playing from my PC or record direct to DAW
Winner: AxeFx (can be used as USB sound device and has headphones socket)
Both the KPA and AX8 can't be used as a sound device interface so you'll need to supply your own interface between them and your PC ( I use a Yamaha MX10XU 10 channel USB mixer - as well as dedicated USB in volume it has headphones socket so I can hear nice 'latency free' mix of both sound coming from PC and from guitar processor).
If just wanting to quickly power up something and hear yourself solo via headphones then both AxeFx and KPA beat the AX8 because the latter has no headphone out - you'd need to make or buy your own cable to use the outputs to headphones (not a biggie I guess).
Portability for live situations
Winner: KPA powered toaster and KPA dedicated footswitch - both fit nicely into a double kick pedal padded case. That and a passive cab of some sort and the rig
could be complete ('could' being subjective on how you like the KPA FX - you might prefer to use your own pedals)
However, an AX8 is an all in one footswitch and processor so portability on that side would be better - BUT you also need either a powered monitor or separate SS amp and your current 2x12 cab to complete the rig to be used as backline.
The AxeFx needs to be racked - however I have mine in a 4U padded rack case along with a Matrix GT1000FX power amp and a front breakout I/O 1U panel and it's very light to carry. The MFC footswitch and expression pedals mounted on a PedalTrain in a soft padded case are heavier and add bulk to the rig as a whole.
Sounds
Winner: I'm going to say AxeFx or AX8 because while there's probably not that much difference between the Fractal units and KPA raw amp and cab tone, the AxeFx and AX8 have serious quality FX built in.
The KPA really needs to have profiles made at all the various gain stages you want to use the profiled amp at - you can try altering the original profile by changing gain and Bass /Mid /Treble parameters via the knobs but you'll be detracting from the original profile by doing so because those parameters are global and nothing like the actual profiled amps' tonestack controls. The Fractal units model the entire preamp and power amp of the original amps so it's capable of authentic interaction between the tonestack eq controls and gain amount etc.
Creating your own profiles on the KPA isn't quite as easy as it's made out to be - if you're serious about it then you'll need decent mics and mic-pres to do a decent job
You'll almost certainly end up buying Kemper profiles - but with the Fractals you just can start from scratch and build your own sound without paying anyone. (You can pay for pre-made presets and third party Cab IRs for the Fractals too if you want)
With the Fractals you just find the amp model and tweak it to taste along with a nice Cab IR (either factory one or buy a Cab pack to use).
Customisation
Winner: the Fractals
You can do some serious tweaking with them like trying different tubes and moving the tonestack eq position around as well as alter all the other geeky stuff that makes a real amp work.
If I wasn't in a couple of live bands and wanted something for home use without too much faffing about I'd probably choose the AX8 and use my mixer and Studio Monitors. Hook the USB from PC to the mixer and I could create loads. It would do quality live playing duty too with the addition of a power amp and cab.
However because I'm gigging fairly regularly I'm well used to carting gear about so the AxeFx or KPA suit me. Or my old tube rig .... or .... (something from 20+ years of collecting stuff
)
Taking all into consideration .... the overall winner of all things I own? The AxeFx. Hugely enjoyable tool to have sitting beside your computer. .... even with a semi-luddite Tool sitting in front of the computer!