Many states in the US have justice systems that are at least ostensibly rehabilitation-based, and to the best of my knowledge many countries in Europe have punishment-based systems. But though we humans always want to make easy black and white characterizations anything involving as many people as a criminal justice system is going to end up as a compromise between various goals.
It was a generalization, there are big differences between the various states in the US, and there are big differences between various countries in Europe, but generally, criminal punishments are less severe over here, and more severe in the US.
Some states in the US have the capital punishment, and some even allow the victims to witness the execution. "To ensure justice was done" is the official explanation, but in reality, it's to satisfy the victim's desire for revenge.
Over here, the victims of a crime are part of the process only as witnesses, and then they're out. There are no juries to sway with emotion, all sentence lengths are standardized by law, and "life in prison" means 20 years, max.
There is no public opinion that we should be "tougher on crime", no political parties are campaigning with the promise to increase sentence lengths or be harder on criminals, some want more resources and money to the police, but that's it.
There's a general awareness that prisons actually harden criminals, that the more time they spend with each other, the more likley they are to return to a life of crime when they get out. We try not to mix people serving a sentence for the first time, with people who are return criminals.
The primary purposes of prisons is of course to lock people up, to remove them from society, to ensure they can't move freely or do work or business, but there is a secondary explicit purpose, and that is to rehabilitate as effectively as possible, to give the prisoners as much help and support as possible, to make sure they don't commit crimes again.
It is very common over here that people who commit murder are sentenced to forced psychiatric rehabilitation instead of prison, and you do psychiatric evaluations of everyone accused of violent crimes, so there's an underlying general sentiment that criminals are sick, not evil.
Of course a lot of people mistrust former convicts, of course a lot of people think criminals deserve to be put away, but there's a lot less of those sentiments over here, compared to the US. Our prison population per capita here in Sweden is also 1/10th of the US average.
So, given all this, the news that a lot of criminal behaviour can be explained by brain malfunction isn't devastating at all. Quite the opposite, it means that you suddenly have more ways to rehabilitate criminals, if you can remove a tumor or fix a chemical inbalance, that's good! It means even less people in jail, and less violent crime.
But if the primary purpose of your justice system is to ensure the victims get their revenge, then it's not helpful, it's not good, because it will "rob" victims of their revenge.
The US had really, really bad crime in the 1980's and 1990's. In a lot of large American cities, infamously including New York, things like street muggings were literally a fact of life that nearly everyone had faced one time or another. I'm not aware that things ever got that bad in Europe; it's not fair to criticize our solution to a problem Europe hasn't even had.
Why were things so bad? We're not a culturally homogenous society, so we have lots of oppressed classes of people who are more likely to turn to crime. We have a history of high immigration and a history of puritanical, prohibitionist laws, which means organized crime from all over the world can easily gain a foothold here.
And, unlike Europe, large parts of America were basically frontier less than 150 years ago. The "wild west" wasn't as violent as you see in movies, but it wasn't a very nice place, either, and harsh measures were sometimes necessary. A lot of American sentiment on capital punishment dates from these times, and these circumstances which Europeans haven't been familiar with for centuries.
Pragmatically, the American justice system (capital punishment and long sentences included) does a very good job at containing criminals. We can be fairly certain that as long as someone is in prison, or dead, they are not going to go on and commit more crimes.
Frankly, the bulk of the problem in America has been urban gang violence. You can't fix that by rehabilitating individuals, because gang violence isn't an individual crime. Sure, brain malfunctions might explain individual criminals. They don't explain entire criminal subcultures. They can't all have brain damage, they just live in a culture where gangs are normal. Any human will do violent and terrible things to fit in with the culture that surrounds them.
As for the jury system, Americans consider jury trials to be just as fundamental to democracy as elections. Of course juries can be swayed by emotion--but if you only allow trained, expert judges to pass verdicts on a trial, by that same reasoning, shouldn't you only allow trained experts to choose your country's leaders? After all, voters can be swayed by emotion, too.
On another note, I'm curious as to how the justice systems you're talking about would handle criminals like Timothy McVeigh or Charles Manson. Don't you think that someone who kills children with truck bombs, or arranges a series of murders in order to incite a race war prophesied in Beatles lyrics, is too dangerous to be let go? A lot of experts believe that true psychopaths can't actually be rehabilitated--at best, they only learn how to fool therapists into believing they're healthy again. How is that handled?
Well, it's a blow to the foundations of revenge-based justice systems, like the US one.
In rehabilitation-based justice systems like the ones in Europe, this is not a problem. It's simply more tools to diagnose and rehabilitate prisoners.