Well, I beg to differ with all those who say it's night and day, the Axe smokes the Helix, and all other versions of the same hype.
I have a Helix Rack with Floor Control
I also have a Helix Stomp
I also have an Axe Fx3 and FC-12
I run both the Helix and the Axe into a pair of PowerCab Plus 1x12s, about 2 metres apart for great stereo. The Helix connects via the Line 6 Link (automatic split into stereo) and the Axe Fx3 plugs stereo into the audio inputs of the PowerCabs. The point being that both the Helix Rack and the Axe Fx3 are running into the same power amp and speaker setup.
In terms of sounds, and I know my ears have lost their youthful acuity, it is level pegging. I can get great sounds out of both, and I can get awful sounds out of both. The UI for tweaking things in Hx Edit and on the unit itself is WAY better on the Helix, especially with Hx Edit expanded to full screen on my 27" iMac (something Axe-Edit still won't do).
In terms of feel, I notice more differences in feel between different guitars than I do between the Helix and the Axe Fx3. I also own several real amps, mostly tube, going back to my original 1980s MusicMan HD 212 - and I really can't pick the difference in feel to any degree of significance between the Helix, the Axe Fx3, and most of the amps.
I also accept that an audience won't hear or feel any difference between any of those units - and they don't care. And differences between IRs are so subtle to an audience in a venue with the room acoustics overlaying everything that it's a waste of time even playing with them. In a studio setting, however (which is my main playing realm) they do make a difference. But once again, I find that the Helix and the Axe are equally good, even when soloing the tracks. But it's horses for courses - there are some sounds that just have the edge on one or the other unit, and that's the one that gets used for that track. But it's by no means anywhere near the black/white difference that so many on here suggest.
If you read the Helix forums, they say the same things about the Axe Fx3 as so many on here say about the Helix. My takeaway from that is that there is so little, if any, REAL difference between them that I'm happy having both or either. When all said and done, it's about the music far more than subtle differences in tone.
Does this make me a heretic?