To the minimal end of shooting, 44 Special can be fit into 5 round medium frame revolvers for conceal carry, a 45 anything cannot. Thus those who want a smaller revolver, and want a big bore revolver, come to 44 Special as the solution. Its helped keep the cartridge itself more alive over the years. On the higher end of shooting, the 44 Special can typically be cooked hotter safely, especially over a long time round count, than a 45 ACP with less concern. Any gun built with proper post war steels will be able to handle maximum 44 Special loads without concern, even far hotter in many examples, the 45 ACP in revolvers is high in standard pressure and going higher is a questionable long term practice.
I've never seen S&W claim that the 45 ACP revolvers are built for +p or 45 Super, even if some handloaders on the internet claim to do so with no issues. Especially on a long term basis, a few 45 Super may not hurt your modern Thunder Ranch, but what about 10,000 rounds from now of cheap handloaded practice rounds? One day those guys might finally push their luck too far. ~22,000 psi 44 Special rounds in a post war 44 Special N frame, or a new M69, or through my M29, is a feat that can be produced perhaps a few hundred thousand times with no threat to the cylinder. I would not like to do that to my beloved range queen M-22, which I have handloaded for and shot many thousands of times.
44 Special looks worse today than it really is because SAAMi hamstrings it with a 14,000 MAP because of old prewar steel guns and 45 ACP looks better because its MAP stays much, much higher. The irony being that this should be the opposite case in most postwar, well built revolvers. This gives the 45 ACP equality/superiority on paper within established theoretical limits, not taking into account all other factors. In a way, this is just plain unfair and makes one looks worse than what it is; with people pushing their luck on the other cartridge it makes this unfair comparison more unfair.
Down the middle of the road is where the 45er' probably wins. As in "if you are going to carry an N frame revolver, and you are going to choose between standard 45 ACP and standard 44 Special loadings, the 45 is as good if not better" you can make a great argument. The 45's bigger bullet gives it the tiniest of edges, its shorter cartridge, or the 45 AR's, means easier loading and extraction. If i exclusively carried 44 Specials standard SAAMI reloads in my M29-2 you would have a great argument telling me to carry my 22-4 1917 instead, I've got a hell of a 255 SWC load for my 1917. The argument i should carry my 1911 instead would be stronger. This is where OP's question probably finally lands us.
In the end, I think the medium power 44 Magnum or hot 44 Special is probably, with the right bullets, one of the best choices for shot for shot terminal performance, general carry for hunting, barrier penetration. This is where my M29 leaves my other N frame far behind and the 45 argument becomes moot.