I've had both the P3AT (had it, traded it in for the Bersa) and have a Bersa T380 (Concealed Carry version) right now.
P3AT Pros and Cons:
The P3AT is the most concealable pistol in 380 or bigger I've ever seen, bar none. A spare mag is the size of about 5 sticks of gum. The gun is TINY (that's a good thing), put it in a #2 Uncle Mike's pocket holster and it'll print less than a small cell phone in your pocket would. They make a neat little belt clip (like a pocket knife might have) that can clip the pistol to the inside of your pants. Just about every other pistol (other than a NAA22) will be too big to do that.
Many people report having very reliable P3ATs, sometimes new out of the box, sometimes after some fluff 'n buff. Mine was a used P3AT and it jammed too much, which is the main reason I traded it in after a week or so of shooting it every day.
The P3AT has snappy recoil, which there's no getting around because the pistol is so small and concealable. I still have the scar on my right thumb where the tang kept hitting the same spot over and over. You probably won't want to shoot much more than maybe a box of 50 in one session with the P3AT.
I traded my used P3AT in and bought a NIB Bersa T380CC which I still have. The T380CC is a little bigger than the P3AT, but it conceals and carries just fine in an Uncle Mikes #3 or #4 pocket holster. It's a nice little gun with a few features that you normally don't find on $300 or less small guns, like conventional safety and DA/SA operation, a loaded chamber indicator, slide locks back on last round (the P3AT does not).
I like the Bersa T380CC, but mine is now the backup to the backup gun (#3 in my stable of carry guns, my preference these days is to carry either a 357 snubbie or a compact 9mm if I can over the 380).
The only cons IMO about the Bersa are that I think it's kind of lightly and a little bit cheaply made, despite the nice features it has. I'm not knocking it. But 1) for instance in order to seat a magazine by rapping the base of the magazine, the impact always causes the slide to pop forward if it had been locked back. my other autos don't do that unless I just slam the bejesus out of the magazine. Also 2) the magazine release button gets sort of stuck from time to time. It can be kind of difficult to get it to release a fully loaded magazine. And 3) occasionally after I rack the slide and decock the hammer, when I put the safety back to 'fire', the trigger does not always engage the inner workings sometimes unless the slide gets jiggled. For this reason if I do carry it, I always put the safety on 'fire' and verify that the trigger is engaged. I'd really hate to draw the gun in need and then find out the trigger was just flapping in the wind. Some people find the safety action lever to be really really tight and hard to operate. Mine was hard to use when I bought it, but after a couple of range sessions it eased up and hasn't been a problem on mine.
The pistol works ok, but imo it takes just a little fiddling and several hundred rounds to get used to it's pecadillos. I think these pecadillos are just because it's such a small and light pistol. The Bersa T380CC is pleasant and accurate to shoot. But, nice as it is and even with the devoted following it has (check out the Bersa chapterhouse sometime), it ain't a Rohrbaugh (spelling?)