Importance of a thru-axel for mountain biking Looking at two fairly similar mountain bikes.  On the rear wheel, one of them has a thru-axel and the other one doesn't.  What kind of effect will this have on the bike's handing and how important is this?  

Kona Big Honzo has a thru-axel (link): 



Norco FLUID 7.2/6.2 HT+ doesn't have a thru-axel (link):
The industry has gone through axle as they do have advantages. The dispute I have with the marketing is how much difference that advantage is. Through axles have advantages only if every thing else is equal. Like most things bikes, quality of construction is more important than style of gadget, so a QR on a quality hub will outperform a Though axle on a lower quality hub.  

One reason to go Thru axle is if you think the look is important. 

For actual riding, all else being equal, go for the thru axle. But I mean 'equal equal'.  If you have got to the point you are going to flip a coin to decide kind of equal.

Edit: 
Advanatges of thru axles


Stiffer - less important on the rear axle, helps with more precise and predictable steering 
Stronger - only an advantage if you are in teh habit of breaking axles. 
Captured  - cannot be ejected by disk brakes, although problem solved with 
lawyer lips


Disadvantages


To remove wheel need to remove axle. Lost axles/axle left behind do occur. Many Axles are propitiatory - lost axle means bike off the road till manufacturer supplied one arrived, days and $$$$.
takes longer to change a wheel - if 10 seconds matter to you, QR may be better
Some need tools to remove and install. 


Keep in mind when reading internet about advantages of Thru axles, many reviewers base their description on a new bike (or fork) vs old bike (or fork), and attribute all the change to the through axle. Those that do robust comparisons are professional riders. Most riders will not feel the difference. So in terms of what you have asked - there will be no practical difference between the bikes because of the rear axle.