Here are my subjective impressions having owned both speakers (though not compared at the same time side by side). These were sent in a PM to another head-fi user:
I've owned both the audio engine A5's and the Airmotiv 4's. They sound very different. I would actually buy both of them and compare (if you can) because they both have a no questions asked 30 day return policy. The A5's are definitely a warmer speaker. They may go a bit lower than the 4's, have a little less-controlled bass, and they have more of what I would call a "lush" sound. The A4's on the other hand have a more detailed midrange (cymbals and strings/voices sound amazingly clear). This can make you think that the sound is a bit thinner, but it's actually just neutral. I do miss the lushness of the A5's, but the airmotiv 4's have grown on me a bit. With the 4's you can dial down the tweeter if you find it to be too bright. You can also dial back the bass as well. So that's a nice feature. I haven't played with these eq's yet since I just moved. Another thing to consider is that the audioengine a5's aren't as finicky about placement, whereas the airmotiv 4's require some playing around with toeing in or out, moving forward or backward. Overall, I think the airmotiv 4 is a better speaker and probably a better value, but the two do sound very different. I listen mostly to rock and acoustic, but techno might sound fuller on the A5's. But with the 4's, it's like a veil is lifted from the midrange. Your best bet is to get them both to compare.