Since both companies have a 30 day trial, it may be worth your while to order both and make a decision that way.
As for differences between amps, of course they sound different; just because some people can't hear a difference, it doesn't make it so. All that matters is if
you can.
There are many blind test proving that some people can hear a difference; for example
this one, done with 500 people.
Even in the test JohnK pointed, there is a "small print" of sorts at the end of page 5 stating that the results don't mean that a particular listener might be ale to distinguish one amplifier form another.
By that token, I can suggest not wasting your money on either amps you're looking at; there is a amp - Behringer EP4000 - that sells for $380 and is capable of 1,400W into 4 Ohms per channel, putting both Emotiva and Axiom amps to shame (and many, many others, more expensive). It's got LOTS of power, it's cheap, and since there is no difference between amps I don't really see why anyone would buy anything else.
It can also be bridged, delivering a whooping
4,000 W into 4 Ohms!
