I have two 10mm handguns, a Glock 20 and a Dan Wesson Bobtail Commander.
They are wonderful guns and a great caliber. The 10mm was originally developed to provide performance similar to the .41 Special revolver round in a semi-automatic package. It started to take off after FBI weapons evaluators determined that it was the FBI's "round of choice" to replace the 9mm, which was deemed to lack sufficient barrier penetration capabilities.
The FBI was comparing round capabilities after firing through a range of barriers while weighting weapon types by capacity. However, after the first 10mm weapons were delivered to the FBI, they changed the specs for the round due to "controllability issues" - basically poorly trained FBI agents had trouble qualifying with the full power 10mm ammo they were issuing.
In the end, the specs for the FBI version of the 10mm allowed S&W, who didn't have an existing handgun with a frame long enough to support the 10mm round to develop a shorter round that would cycle in their shorter action. The .40 S&W became the FBI round of choice and glock then beat S&W to market with the Glock 22 and Glock 23 as the first production guns chambered in the new caliber.
So, why is 10mm better than .40 S&W? You can down-load a 10mm to the exact same specs as a .40 S&W or you can push the round to carry 20-30% more energy out of the barrel. The longer case is almost more forgiving with heavier bullets where the .40S&W can quickly over-pressure with 180gn bullets if they're set-back a little too far.
A 10mm round can be loaded hotter than a .357 Magnum and a 15rd Glock 20 magazine can carry more energy than a 6rd .44 Magnum cylender.
Plus, you can pick up a .40 S&W conversion barrel for a Glock 20, allowing you to shoot less expensive .40S&W ammo while still having the option to go full bore with 10mm rounds.
S&W did build a 10mm for the FBI, the 1076. They already had a large frame pistol on 10mm, the 1006. Problems ensued because the large frame was cumbersome for those with small hands.
The choice of 10mm was political according to some of my friends in the business at S&W. One faction in the gov't supported the .45 and another wanted the 9mm, so the 10mm was a compromise. The compromise was short lived due to handling problems (see above) and the recoil of the 10mm. The recoil problem was solved by issuing rounds that resemble to .40. Also, there were problems with the 1076 which was rushed into production, leading to QC problems.
The hard fact is that a full power 10mm round (200gr at 1200fps) is too much for most shooters, including the officers it was issued to. The mention of the .41 mag gave me a chuckle; it never went anywhere in LE, most likely for the same reason.
The .40, which is the greatest round in the world, was the final compromise. Why use a long round requiring a large frame when you can get the performance you want out of a short round in a smaller frame? The rest is history; the .40 proliferated and the 10 languished.
Before you 10mm afficianados get your knickers in a knot, hear me out. I think the .40 is the greatest round to come down the pike because of its role in competitive shooting. This round is extremely versatile and performs extremely well in IPSC competition as it can be loaded to major velocities for limited class, but is small enough to fit 20 rounds in a mag. You just can't do that with a .45.
Also the .40 is cheap to shoot. Brass is free on the ground at your local range and the .40 offers the option of lighter bullets (180, 165, 155, and 135) than the .45. Most of your .40 loading can be done with fast burning powders like WW 231 which are relatively cheap. I can duplicate the performance of a 200gr .45 round in one of my .40s and save about 25% . This allows you to practice on a 1911 platform for a lot less money.
Unfortunately the .40's claim to fame is in the practice/competition area only. I love this caliber and use it for about 75% of my shooting but wouldn't consider carrying a .40. I much prefer my 5906 loaded with 9mm CorBons (147gr hollow points at 1100 fps) or the venerable .45 ACP in my new M&P.