Hello. I agree with Erich. The striker-fired Browning does not have any sort of "half-cock" notch or internal firing pin safety. If parts are out of spec or worn and the gun receives a knock, it could be possible for the striker to fire the gun inadvertently. Of the two choices you gave, I'd go with the Walther, preferrably a French/German one. Some of the American ones I've seen, owned, or shot over the years did not have stellar reliability. Some worked great.
I wouldn't carry the Browning. I had one, and loved it, but wouldn't carry it. Like already said by others, I wouldn't trust it, but that's not the only thing against it.
The thumb safety is very small, so besides being easy to "miss", it doesn't give you much leverage to take it off. It isn't that hard to move, but you just don't have much to move it with.
The sights are almost useless on the Browning. I said "almost" because there may be someone who can use them. I could not, and never found anyone who could. Walther sights aren't the very best, but they are fantastic by comparison.
I believe that you would have been better served by purchasing the Bersa .380. It would be a new pistol and have better ergonomics than the Walther. It was your choice, but I personally feel better served by the South American import. I love mine!