All three are different from one another quite a bit. The L-A1 and MR9 are both striker models. The MR9 and AZ (like Sig 226) are both DA/SA but, the AZ has a hammer.
I've not shot the AZ but have held one once. I have a few mags through the MR9 and it was a pretty good shooting gun not unlike the Walther P99AS. I've shot quite a few current Steyr's. Most of them were the shorter M_-A1's. I also own a L9-A1.
As a group their accuracy is exceptional and reliability has been perfect. The Steyr's have one of the best striker triggers overall. They are in a group with the Walther PPQ, Sig 320, and HK VP9. The reset could be a little better on the L9-A1 in terms of being more tactile and a little shorter (like the PPQ). The trigger tab is unlike most others in that it does not pivot but, pushes straight in. It's a less obtrusive design. They have a more muzzle heavy balance point and the grip is more forward. It also has a very low bore axis. These all add up to create a gun that has low recoil/muzzle flip. They don't have adjustable grips but, I've never heard any one say that the grip was uncomfortable. The would range from guys with big hands to kids and women with smaller hands. The grip angle is very Glockish which some don't care for. The trap sights are different and took a magazine or two to get used to. I prefer 3 dots but, have no issues shooting these along side 3 dots. That's something that can be changed out.
I don't have any issues with holsters and there is some aftermarket support as well. CDNN has 15 round magazines for reasonable prices.
The L9-A1 is my second favorite striker pistol currently made. It is aesthetically unique and pleasing to my eye. I think the current Steyr lineup is underated but, like any brand/model not for everyone.