So none is better or worse in terms of interaction with the new Axe-FX.
That isn't really true... Many midi controller pedals cannot natively do scene changes, which means they also cannot do channel changes... Meaning they are not as well suited.
So, the ones that would work well in general:
Liquid Foot
RJM
BJ Devices
Gordius
Voes
Morningstar MC-6
MFC-101
The above controllers have various levels of programmability and other features you may or may not require.
Avoid the Ground Control pedals... They definitely are a poor choice for scenes and won't work for channels.
I don't think the Midi Mate supports defining CC data values, so another one to avoid (might need to check the manual).
The same for the Tech21 stuff...
The key ingredients you need:
Ability to send PCs (for preset changes)
Ability to send CCs (for IA switches)
Ability to define what CC data value is sent (for scene and channel selection)
IMO, you already have a capable controller. It's not as programmable as maybe an RJM or Gordius, but until the other controllers are updated for two way communication with the Axe Fx III then none of them is going to do things like display the tuner, automatically display the preset name, track IA states across scene changes, etc.
Edit: one more capability you really want:
the ability to "group" switches to make them mutually exclusive. Otherwise tracking the active scene could be very confusing. Alternatively, a feature like on the Gordius which allows you to assign LED state on button press works, too.