In addition to running, I ride bikes. You may have figured that out based on some of my bike posts here. Anyway, I figure bikes are a much easier way to show this, since suspension is easier to visualize than EVA. So I generally use mountain bikes to explain responsiveness.
|Yeti 303 RDH|
The bike in the picture above is a downhill bike. Like a premium cushioned shoe, it's incredibly plush and super forgiving. However, all that travel and plushness comes at a price. If you try to pump this bike with the terrain, the response is delayed slightly. You pump...then the suspension compresses...then the bike pumps into the terrain...then the suspension uncompresses...and finally you get your response. There's a reason you don't see people riding 8" travel downhill and freeride bikes on pump tracks or using them to dirt jump. The shoe that I'm currently wearing that matches up the best with this bike is the Brooks Ghost. Very forgiving and plush, but the response is somewhere between slow and nonexistent (that review I linked to is the 3...the 4 seems to be even less responsive, but then again, it might be perception based on the other shoes I'm currently rotating it with).
|Blk Mrkt Three57|
|Blk Mrkt Killswitch|
Of course, I don't want you to think responsiveness is limited to racing flats, just like bike responsiveness isn't limited to dirt jump hardtails and BMX bikes. This is a full-suspension dirt jumper...and if anyone wants to buy me that bike in the picture, I will love you forever. You've got a little bit more forgiveness and plushness than with the Blk Mrkt Three57 hardtail (though it's nowhere near as forgiving or plush as that Yeti 303 RDH in the top picture), but it's still a bike with a super fast response. The shoe I have that best embodies this is the Mizuno Wave Rider.
One thing I do want you to be careful of is not confusing cushion or stack height with responsiveness. The bike in the picture above is a 4" travel XC bike, meaning it has the same amount of travel as the Killswitch in the picture above. However, due to the geometry of the bike and the lower pressure of the fork, it's not as responsive. I actually own the bike in the picture above, and when I first got it, I attempted to jump it and couldn't figure out why the timing seemed so weird and why I was hardly getting any air. It's a plush bike and fairly forgiving, but it has very little responsiveness when I compare it to my dirt jumper. It's a great trail bike, but it's way too slow to bring to the pump track. It's the Brooks PureFlow of bikes...the PureFlow works fine to train in, and the plushness is nice for that, but I would not want to race, nor do I want to do speedwork of any kind in that shoe. So it goes with shoes: two shoes can have similar amounts of cushion, but one can be more responsive than the other.
Now, of course the gold standard is to get a well-cushioned shoe that's still responsive. The bike guys do stuff like throwing a stiff shock in the back and stiff fork up front, or they change the geometry, or whatever to try to do it with bikes. Shoe guys have it a little easier since the differences aren't quite as drastic, though we still have a long way to go before we can build a Nimbus that responds like a Piranha. And like anything else, there aren't clear cut categories of responsiveness, but rather a scale with the Piranha on one end, the Nimbus on the other, and everything else somewhere in between.
One last thing to keep in mind is that responsiveness is something that different people define in different ways, so this post isn't law for all reviews, but rather a guide to my own reviews, to try to further help you figure out what shoes are most appropriate for you.