I am admittedly a noob when it comes to speaker tech, but I love great sound. My questions for those of you in the know is the following.
Is there are significant or noticeable difference to the performance of the on wall versus on/in wall design? Does the lack of a back chamber make the on-walls a less desirable choice?

I'm trying to plan my setup and if there is no significant difference, I may go with on-wall for portability if I move.

Cheers!

For best sound reproduction, in wall if at all possible.

On wall speakers are for space (depth) limited applications. Since the internal volume of the enclosure is limited and not optimal, you will not get the best possible sound. It's still going to sound very good but not as good as it could be.

If at all possible, mount the bookshelf M22's on the wall for best on the wall sound, I would mount a painted board to the wall, then mount the M22 to the board. I'm using two 1/2 inch boards glued together so I've got plenty of thickness for the screws. These can go good with a VP150 center, on wall. 2nd choice would be in/on wall M22's, and lastly the on-wall M22's.

I'm in the process of mounting bookshelf M22's above and below my TV, but got lazy and haven't progressed in a while. I really need to get this done. But, seems when it comes to getting things done, it's cleaning the house or yard work instead. Mama Mia!

I've compared my M22's to my onwall 22's side by side and they both sound very similar in the mid's and highs, however, the regular M22's did do better in the lower bass frequencies. This would be expected with the larger enclosure.

However, once you include a sub in the mix and have a proper crossover setting, there is little difference.

I tend to disagree. I believe that there is a hole in the upper bass, that the VP160 helped fill in nicely. Can't really blame that one on the room acoustics, because I'd have the same hole with the VP160.

This was audibly noticeable using the Police's blu-ray concert called Certifiable. Once the VP160 was installed, the upper bass notes that I couldn't hear well before were now there. So, with that said, if a VP160 is at all possible, I'd go with one of those. I bought an in-cabinet model, and installed it below my tv, flush with the wall, pointed slightly upward. But I was lucky that there was a big cavity in the wall there. Those are about 15 inches deep.

Now, to be fair, the Axiom speakers sound wonderful, even with this small hole. You probably wouldn't notice it until you go looking for it. Probably, the only way to get the best sound is to go with M60 and up quality speakers. There will always be some compromises made with smaller boxed speakers, regardless of brand. I doubt that, for the price, you could do better than the Axioms. So, it's not a flaw with Axiom, but, more than likely, a characteristic of a bookshelf speaker that's designed to play as flat and uncolored a response as possible, without growing too large in size.

Anyway, that's my thoughts and experience, YMMV.

To the OP,
Recently looked at the same thing for an upcoming purchase. I am opting for in/on walls. Compare Axiom's specs between in/on wall versus on wall and you will see the in/onwall covers a slightly larger range of freq.

I have the in/on walls and can recommend them if you must stay with an on wall solution. However bookshelf versions on brackets would be even better. Also note that the in/on walls are being discontinued, so can be had at a good savings - so it's a good time to consider going that route.

Yep, just saw the In/On Walls are 20% off.
Just placed my order.

I'm quite happy with my M22 in/on hybrids.