Well no one has taken a stab at this yet so I'll get the ball rolling.
One reason no one has taken it on may be that the question is a broad one, so where to begin becomes a challenge. How do they stack up ballistically? Or in terms of the guns chambered for them?, or etc. You want a short answer or a long.
The long answer:
In the late 1980's the FBI wanted to go to a more powerful handgun round than the 9mm and had begun experimenting with the 10mm. By 1989 engineers at S&W working with their counterparts at Winchester figured that if they shortened the 10mm they could have a cartridge that met the requirements of the FBI for a powerful handgun round and have a round short enough to work in guns designed for the 9mm. Handguns that could in a relatively small design carry more rounds than a 10mm or a .45 but gave you almost as much power. A stroke of marketing genius. The .40 S&W was born. It has in the last 20 or so years become the standard round of many law enforcement agencies and very popular for personal defense.
The .40 S&W is widely available in many good commercial loads. From 135 gr. JHP from Cor-Bon to to a variety of 180 gr. loads in an assortment of configurations. If you handload all bullets available to the 10mm will work as well.
To give you two examples: the 180 gr JHP load available from Black Hills gives a 1000 fps velocity at the muzzle. This is 400 Ft-pds of energy. For a Taylor KO index of 10.3
The Remington 165 Gr. JHP has a muzzle velocity of 1150 with 485 Fpds of energy and a Taylor index of 10.8.
Other rounds and loads offer more power. All this out of a 4" barrel.
There is a trade off of course. The .40 is a high pressure round at or in excess of 35,000 pds. This makes it a snappy round to shoot with a good deal of muzzle blast with most commercial loads. It is a very good self defense load. Most firearms manufacturers offer it in a wide variety of well made guns.
The .38 Super was introduced by Colt in 1929 and was chambered in the 1911 (the .38 Super and the .45 acp have cases of .900 in length). It was derived by supeing up the .38 Automatic. It was sold as both a hunting, self defense round and to law enforcement. It was popular for a brief period of time with some police departments because it could penetrate the steel hulls of motor vehicles of the day and the "bullet Proof" vests some gangsters used. Something the .38 Special could not do. Famous FBI man Melvin Purvis carried a pair on occasion.
From the time of it's introduction to the 1980s or so it was the most powerful round that could be shot out a pistol. There isn't a lot of data for the old commercial loads which were only FMJ or LRN bullets. There were no JHPs back than. But you had a round that left the muzzle in excess of 1000 fps with around 400 ftpds of energy. 158 gr. bullets were often used but lighter rounds were available.
Two things weighed against the Super though. One was that the U.S. till the 80s was a nation of wheelgunners. Even the 1911 was widely mistrusted. So when the .357 Magnum came along cops and handgunners had the power that the .38 Super gave, and more in a form they took to and found reliable. The second thing was that Colt (following Brownings lead)had headspaced the round on the semi-rim rather than the case mouth and accuracy was iffy from gun to gun and round to round. This problem was finally cleared up in the '80s.
Anyway the Super has stuck around. Only a few companys offer decent loads in it though. Only a few offer good bullets in it as well. But they are available. Most load it to around the power of a 9mm or 9mm+P. But it can do much more. Cor-Bon and Buffalo Bore (I believe) are some of the few that offer really good commercial loads. Most ammo companys load the Super with 9mm bullets. Any jacketed or lead bullet for a .357 can be handloaded in the Super.
Cor Bon offers a load of a 115 gr. bullet with a muzzle velocity of 1450 fps for 537 fp of energy.
The .38 Super is a very flat shooting cartridge.
Recoil out a 1911 GM is quite mild with more of a push, than the snap of the .40. Depending on the powders used muzzle blast can go from mild to quite loud and bright with, to me anyway, less bark than the .40. Fun at the range.
The .40 offers more power in a wider variety of handguns. It also offers a wider variety of available commercial loads with bullet weights from 135 gr. to about 200 grs. in a wide variety of forms. It is a snappy round with a good deal of muzzle flash, this is due to the high pressures it tends to operate at. This though can be worked through with practice and it is an accurate self defense round.
The .38 Super can give you the power of a .357 Magnum (in the lower to mid range loads) in a pistol with less pressure than the .357 Sig which means less felt recoil. It can be a very accurate cartridge. For decades it has been a favorite with many handloaders for hunting and target shooting purposes. bullet weights vary from 115 gr.s to 160. Most companys load the round with 9mm bullets, but any .38 or .357 will work. Most companys don't offer the round close to what it can do.
More handguns in a vareity of designs are available for the .40 than the Super.
Tipoc, you leave little room for additional details and specifics of which I find extreamly usefull... Now let me ask you (all), and I know this a subjective question... Which of the two would be the more practical all around caliber 38 Super or the 40 (not brandwise) for protection, shooting, sport???
I want to ask something.
Due the previous answers and other answers I have read from other forums seems like the modern .38 Super is a balistic twin of the 9mm Luger, is it true?.
I meant seems like the .38 Super loads are not in the present days what was used to be in the past.
Forgive me if my English is not good enough.