I used to have a P3AT, and really didn't like it that much. I don't mind heavy recoil, but I didn't like how small the space inside the trigger guard was, and I kept barking my knuckle every time I shot it. I don't really carry a BUG most of the time, but when I do, or when I need a "walk out to the mailbox" kind of gun, it is typically my G43......which you say you don't like. But before I bought the G43.....and the PM9 before it.......and the P3AT before that.......I bought (and still own) a
S&W M&P340.
Now, here's the deal with this gun.......... this is a scandium framed revolver with a stainless cylinder. It only weighs 13.8 oz unloaded, and it is a .357 magnum. A lightweight practice .357 load like 110 grain WWB is not that bad in it. A 125 grain Critical Defense .357 will sting your hand a bit, but not so much that you'd be afraid to shoot the gun in extremis.
DO NOT FOOL WITH the full house 158 grain White Tail Hunting Load under ANY circumstances!
Now, that said, the advantage of a .357 snubbie is of course flexibility. You can download to any soft-shooting .38 special load you want; OR, you can upload to a serious large animal stopper if you're carrying it on a backpacking trip. Downloaded to .38 Special, it has no more and no fewer of any of the sins of the same gun chambered in .38, but you have more options.
Also, this gun comes with VERY good sights for its type - a typical rear channel in the topstrap, and a very bright Big Dot front sight. It's actually easy to shoot well and acquire a good sight picture.
ALSO.....and not to be diminished...... this gun is enormously expensive! MSRP is $869.00. I paid about $750 or so for mine at CTD in Ft Worth about 6 or 7 years ago as I recall. I've had it for a while. There are cheaper versions of more or less the same thing from other manufacturers.
A couple of things..... As a BUG, the "hammerless" design works real well, but not so much as a "kit gun". If I were to buy another snubbie, I'd probably buy something with a hammer, to make shooting single action an option, and I'd be less worried about weight, and more concerned with weather proofing. Maybe something like this:
Ruger SP101 #5718.
Mind you, I'm not trying to talk you into getting a M&P340, although I think it is a very good gun, but I think that snubbie fits your bill. I'd buy one in .357 simply for the caliber versatility. It doesn't mean you have to carry magnum loads in it. And I'd buy one with a hammer (you can always bob it) for the SA/DA versatility. You have to decide if you want to make it a steel or alloy framed gun. Obviously the steel will weigh more, but recoil will be easier thanks to the increased weight.