Remington would have to be manufacturing experience and quality. They made good guns. Colt came along and made excellent handguns, although it took two tries to get them marketed successfully. Sam Colt is a classic example of an inventor who succeeded by perseverance, not luck. Those of you who aren't sure what I am talking about should look up the Colt - Paterson revolver.
Smith and Wesson is another example of perseverance on top of design that triumphed. Although they patented the pass through chamber, it took years to settle the claims IIRC. Even then, they made the thing in .22 Short. It was novel, but I suspect that it was little more than novelty back in its day. We already knew about large calibers and the debate over bullet diameter is nothing new.
Remington played with semi automatic pistols until well after the turn of the century.
Their last repeating handgun was the 51, a .380 supposedly used by George Patton. Of course, they produced 1911A1 pistols for the USA in World War II.
Savage produced some handguns, but they seem to have left that business for the long arms trade, the same as Remington. They made some pocket pistols, among them the model 1905, 1907, and 1917. These were .32 ACP caliber pocket guns and they sold well enough.
Not long after the turn of the century, two things happened that affected Savage and Remington. First, John Moses Browning left Winchester because Winchester wouldn't give him a percentage of Model 11 shotguns sold. Browning went to Fabrique Nationale and Remington ultimately obtained the right to make the gun as the Model 11. This is the Browning Auto 5.
Second was a turn against handguns. The Sullivan Act was passed in New York State in 1911. Other states and cities passed anti handgun laws around then. The pocket pistol was seen as a weapon of the criminal class. This probably influenced some of the more famous makers to get out of the business rather than be associated with an undesirable aspect of shooting. Other companies stayed with the pocket gun trade. Iver Johnson made shotguns and compact revolvers for decades, but the revolvers were not very well made. There is actually a plethora of small makers that produced pocket handguns until about World War II. Savage and Remington were both based in New York State.
Remington also secured the right to build Browning's Model 8 semi automatic hunting rifle. This rifle worked, unlike many semi auto designs of the day. It was sold as a hunting rifle and I don't know why Remington never submitted a modification of it for the Army rifle trials. Remington also made Model 1917 rifles for the Army during World War I, which were patterned after the British SMLE. These were the more common rifle in World War I. The Springfield Arsenal couldn't produce 03-A3 rifles as fast as Remington and Winchester could make 1917s.
Both companies played with handguns through the 20th century. Remington made the XP-100 bolt action pistol and Savage made the Striker, of the same configuration. These are heavy and large handguns that fire centerfire rifle cartridges. They are intended for silhouette shooting and handgun hunting. I think both are out of production right now.
In general, I think that Remington, Savage, and Winchester chose their markets and produced accordingly. Hindsight being 20-20, it's safe to say they made the right decision.