I don't have any experience with the Stoeger, so I can't help you there.
I have owned a PX4 in .40 S&W for almost four years now. To date, it's been the most reliable semi-auto I've ever owned. At one point I'd shot 2,800 rounds through it without maintenance of any kind except wiping down the exterior after each range session without incident. Your mileage may vary; I've heard some stories about reliability issues with the PX4, it just hasn't been my experience or the experiences of my three buddies who also have Storms.
When I first bought it, I found the gun a bit over sized, I thought the bore-axis was a little too high for me, and I thought the guns overall looks were a bit strange.
Then I started playing around with the modular grips. It comes with different size grip panels (don't know what else to call them), which at first I thought would be merely a gimmick. Turns out they actually can significantly change the ergonomics of the gun. I found the small set worked best for me, and the gun instantly felt better in my hand, pointed better for me, and that high bore-axis thing seemed to go away.
As to recoil and accuracy, whether it's the rotating barrel or not, it's my softest shooting .40 cal. And the gun is more than adequately accurate for defensive purposes.
The gun breaks down Glock-style, and general cleaning and maintenance are straightforward.
As much as I like the gun there are some drawbacks. There's not a lot of aftermarket stuff for it. That includes holsters; you have to do a bit of looking around. Also, the DA trigger pull is rather long and heavy and the trigger itself is set fairly far forward. If you have smaller hands this may be an issue, unless the smaller grip piece works out for you.
Hope some of that helps.
P.S. I should've added that the decocker/safety on the Storm is not ergonomic, at least for me. Multiple slingshot racking of the slide can be painful. Also, if you get sloppy with one you can actually flip the thing down, requiring the shooter to have to flip it back up into the 'Fire' position before you can get back to work. It's a relatively minor issue, but it does happen.