Ladder bracing is created when braces are parallel with the bridge, so if you look at the back side of the top, the braces look like steps in a ladder. There usually are not many, 3 or 4, maybe 5. They create fulcrum points where the top can easily vibrate in short, low amplitude motions that are well suited for producing high notes, which therefore get emphasis, along with high overtones from lower pitched notes. Thus ladder bracing supports what is called the "long dipole", though there are more than two poles (spans) created. Highs increase the carry and make the sound more assertive. To get the assertiveness, the top might sacrifice complex, precise lows that a well built X-braced top can provide. Yet, when well built and properly strung, ladder braced guitars make lows that are rich and satisfying, just as compelling too, but in a different, coarser, more "growly" manner. All this qualified, I hope the reader understands, by the difficulty I have putting words to what I hear.
Assuming two tops with the same before bracing stiffness, ladder bracing tends to produce a less stiff top because there are fewer braces and they do not create much triangulation. Thus the energy transferred by the strings to the top can move it further, creating a louder sound, along with the emphasis on treble which makes the sound carry better. Of course, a thoughtful X-brace builder can conpensate for the difference in loundness by either starting with a less stiff top in the first place, or adjusting the stiffness of the braces.
Some say ladder bracing came to be because it was easier to execute in a factory environment. Others say the Italian artisans employed by Oscar Schmidt (one of the early guitar factories) were simply accustomed to doing tops this way, since the lute and early parlor sized guitars were made this way in Europe. There is probably truth in both theories. In any case, it is fortunate that Oscar Schmidt continued using this system as he ensured that the particular sound it supports did not disappear as X-bracing gained wide spread adoption.
Many contemporary ladder brace builders copy old designs without many essential changes, except to build them lighter, with more playable necks, better sounding wood, tighter construction standards, and so on. Those improvements can add up. The blues are a natural fit for these instruments, as they were for the earlier ladder braced guitars. Since flat pickers value loudness, a large bodied ladder braced guitar might suit their playing better than the X-braced dreadnoughts they now prefer, though it might not have the "thump" they like too. Likewise the assertive nature of ladder braced sound could compete better with that of banjoes and mandolins that often join with guitars in bluegrass bands. But ladder braced dreads do not appear to exist, except in the form of Harmony H1260 Sovereigns built from 1958 to 1971. The Sovereigns were fairly loud, but lacked through-the-top-bridge pins, which hampered the coupling of the strings to the top. They were also rather heavily braced. That said, many still consider them the best ladder braced dreadnought guitars ever built in a factory. In truth, they may be the only ones.
Carl Holzapfel built large ladder braced instruments in the very early 1900s and his son continued to build his designs into the 1950s. Their shape resembled the Spanish classical more than the American dreadnought, despite their size. They featured 12 fret necks and 25.4 inch scale lengths, while the larger ladder braced Stella used a 26.5 inch scale. The shorter scale suits steel strings, in general, better than the longer scale, though the Stellas are often tuned down. Holzapfel never paid much attention to playability, carving hugely thick necks that might never warp, but never would facilitate quick fingering. His tops too were hugely thick, .25 inch of more, when a normal X-braced top could be less than half t hat. The instruments built by his son often used pine - not a standard tonewood - for the top as well. Despite all the oddities, they are well regarded for their sound and many contemporary makers use their basic design as a starting point, without apology.
Pre-war ladder braced instruments by Oscar Schmidt, for instance, are priced way below instruments made by Martin and Gibson from the same time period. A few of the most sought after approach the size of a dreadnought, but most are smaller and most are used to play the blues, at which they excel. Before 1939 these carried the brand name Stella, but the name was then bought by Harmony and attached to their most basic and heavily built entry level guitars. These later "Stellas" were neither as expensive nor as well built as the Oscar Schmidt Stellas. Huddie Ledbetter, known as Leadbelly, played a 1935 top-of-the-line Oscar Schmidt 12-string Stella, not one of the subsequent Harmony versions.