I can tell you why I prefer inertia.
I went into this quite by accident. I bought the Stoeger simply because I liked how the gun felt and handled to me and the price was right. I decided o take a chance without fully understanding the differences. I'd had gas guns in the past, Rem 1100's, 11-87's and a Beretta 390 as well as pump guns and double guns.
It was only AFTER buying and using the Stoeger that I came to appreciate and like the inertia system. Compared to the 11-87 and Benelli I still owned at the time the Stoeger was lighter and more lively in my hands. I quickly improved on my hit percentages compared to all others.
Not long after buying the Stoeger is when Benelli upgraded to the M2 over the M1. I ran across a guy who had a 1 year old M1 that just had to have the new M2. He sold me the M1 at a great price.
For about a year I had the Stoeger, Remington, Benelli, and Beretta shooting them side by side. Within a few months I simply stopped using all of them except the Benelli. I eventually sold all of the others except an 870 pump.
The inertia guns in my experience are as simple and reliable as any pump, but with the ability for faster repeat shots. They do recoil more than a roughly 1/2 lb heavier gas gun. But no more than a comparable pump or double and no one complains about the recoil from them.
They are less dependent on barrel length and ammo power. So far I've never had an issue with any ammo in either the Benelli or Stoeger. The 11-87 in particular was quite picky with lower power ammo. All of the gas guns are set up to run with a particular barrel length. If you want to run a shorter barrel expect issues with lower powered ammo. Not a concern with inertia guns.
If I were big into the clays games I'd probably prefer a gas gun. When you're the type of shooter going through cases of ammo each month the added weight and recoil reduction of recoil from a gas gun would add up over time. But for the volume of shooting I do, particularly since I carry my shotgun up to 10-12 miles in a days walking the woods and fields a lighter, quicker pointing gun is far more valuable to me.
so in my opinion, recoil operated guns needing something to push against aren't a good choice.
I keep reading that, but both my Benelli and the Stoeger will function when fired from the hip. The 11-87 gas gun is the one that would not.