This is my off-the-cuff thinking on why some systems seem to reproduce the "attack" of a snare drum or the like better than others. Spoiler: it will have nothing at all to do with a driver being "fast" versus "slow". Disclaimer: I am not an expert, and I'm sure (and hope) that someone more knowledgeable will be along to correct any mistakes in my thinking (or slap me down if I'm entirely wrong).
Horns/compression drivers are often described as being superior at delivering the "attack" on drums and the like compared to other speaker types, as demonstrated by
@Pareto Pragmatic bringing up their Heresies earlier. What horn-loaded speakers actually excel at, in my understanding, is sensitivity/efficiency. My thinking is that drums and like have a large amplitude spike on their attack, requiring large dynamics from the speaker/amplifier system. Due to their inherent efficiency, horn-loaded speakers are less likely to exhibit severe distortion and/or compression when reproducing these large-amplitude "attacks", which is what actually lends them their realism relative to other speaker systems.