I have the FN HP-DA, as marked and marketed in Europe, while the Browning BDA was the same pistol marketed in the US. It's the pistol in the middle. It was developed for the second round of the XM-9 trials, but obviously lost to the Beretta 92. IMHO that's unfortunate, but then I'm a Hi Power fan and absolutely hate the Beretta 92 as it just doesn't fit my hand, and its larger than a full size 9mm Luger pistol needs to be.
The Browning BDA/FN HP-DA shoots about like you'd expect a double action de-cocker equipped Hi Power would shoot and with the exception of the longer DA trigger reach and pull, it feels like a Hi Power if you put comparable grips on a Hi Power.
The pistol on the bottom is an FN SFS Hi Power, with the "Safety Fast Shooting system designed for the Hi Power in preparation for the first round of the M9 trials. It was administratively disqualified as it was not a double action design. That's unfortunate as it accomplished the intended goal without straying too far from the single action 1911 operation that troops were familiar with.
The safety is applied by pressing the safety lever up, which drops the upper half of the two piece down on to a hammer block, while the lower half of the hammer remains cocked and locked. When the safety is depressed the hammer snaps back in the upright position. The modified spur on the hammer also eliminates the hammer bite some users experience with the Hi Power. It's a very good system that also gives the Hi Power a very positive safety feel, as well as an ambidextrous safety.
The pistol on the top is the Browning BDM. It has a dual mode switch (thus the "BDM" name) on the left side of the slide that allows if to operate in normal SA/DA mode, or a DA only "revolver" mode. It was developed for FBI service pistol trials but wasn't adopted. If you ever shoot one it's pretty easy to understand why. It's the thinnest double stack magazine 9mm Luger pistol I've ever handled, but it just feels odd in the hand, and note the "up" decock lever position withe the hammer decocked.
The BDM spawned the BDM-D which is a decocker equipped version as well as the BRM which was a DA only model.
The BDM and HP-DA are interesting variants to own, but my Hi Powers are what get shot.