The .357 Sig continues to flourish because it has been adopted by many law enforcement agencies. According to Massad Ayoob in the March/April 06 American Handgunner, over sixteen per cent of state-police agencies use the .357 Sig (p. 22). This figure puts the round second to the .40 S&W in popularity with law enforcement. It has performed well in the field and is chambered for a variety of compact and subcompact pistols that are easy to carry. Among private citizens, from what I have seen in my own parochial experience, the .357 Sig is not popular. When I worked in a gun store, I met only two people who carried a pistol so chambered on their permits.
As for the 10mm Auto, it has survived despite being quickly adopted and dumped by the FBI and other agencies. The pistols for it are larger and fewer in selection. Glock deserves much credit for keeping it out there when no one else would. Other manufacturers are coming around to it again, so, if you want something in 10mm Auto, you have a better choice now than five years ago. For me, the 10mm Auto is a sentimental favorite because I remember when it came out in the 1980s and eagerly followed it rise and fall in the gun press. I also think that for a handloader it is an excellent choice for a versatile cartidge of many uses. It has managed to hang on despited little, if any support from law enforcement. For better or worse, law enforcement and military sales drive the handgun business in the U.S. If law enforcement does not want it, do not expect much attention from the industry. Despite this situation, the 10mm Auto and the .38 Super Auto cartridges soldier on among sport shooters, but the rounds are not tearing up the sales charts with success. You can see this result in the modest selection of ammo and pistols for each.
What is better? My guess is that they are pretty much equal in performance, but the 10mm Auto offers more choices for bullet weights. For this reason, I prefer the 10mm Auto.