I'm not sure if people really understand what 'stunning' means. It sounds so nice - kind of like an anesthetic before an operation. But in fact it is quite nasty. They basically shoot a captive steel bolt through the brain of the animal and thereby 'pith' it. Alternatively, for smaller animals, they place electrodes on the animals head which 'stun' it.
If you have a very strong stomach you can watch these youtube videos of electric- and captive bolt-stunning. Or you can take my word for it.
(For chickens they spray them with electrified water (stunning) before ripping off their heads. I've seen these machines back in New Zealand. If I was a chicken I'd definitely prefer shechita - but I'm glad I'm not a chicken at all!)
Since 'stunning' makes the animal into a treifah (an animal that would not live for 12 months), it is impossible to halachically pre-stun kosher animals.
There is no evidence (that I know of) that shows that this is less painful for the animal than shechita. But it does have a couple of other advantages. Firstly, the animal doesn't kick around after it has been stunned. After shechita the nervous system of the animal causes it to kick and move for several minutes afterwards. Because stunning affects the brain, the nervous system shuts down and the animal stops moving straight away. This is very important for the guys holding the chainsaws who have to cut the animal up after it has been killed. (For this reason most kosher meat is stunned - but only after it has been shechted.)
Another difference is that the blood stays in the body, which changes the flavour of the meat. Kosher meat tastes saltier, because of the kashering process, but also has less blood in it, so does have such a 'rusty' taste.
The real reason for the labelling is to limit the spread of fundamentalist Islam in Europe. The irony is that many Muslims will allow pre-stunning before halal killing (it is a machlokes, but I think the majoriy in Europe follow this opinion - but I'm not an expert on this). So in practice this legislation will harm Jews more than Muslims.
And the reaosn it makes a difference (because you would think that most kosher meat goes to Jewish shops, and thus doesn't make a difference) is because Ashkenazim do not eat the hindquarters of animals. Therefore they have to sell half the animal to the non-Jewish meat market. Labelling it as non-stunned will make it harder to sell the hindquarters and therefore put up the price of kosher meat. Whether, ultimately, this will cause the Ashkenazim to re-introduce the halachos of removing the gid hanashe (sciatic nerve) and eat the hindquarters - as most Sefardim do - remains to be seen.
Another irony is that the EU legislation is exactly the opposite of what Rambam writes as halacha. In Hilchot De'ot (2:6) he writes:
לא ימכור לגוי בשר נבילה בכלל שחוטה, ולא מנעל של מתה במקום מנעל של שחוטה.which translates as: "A person may not sell meat from a non-kosher animal to a non-Jew and claim that it has been shechted. Nor a shoe made from leather of an animal that died from natural causes in place of a shoe made from leather of an animal that was shechted."
So we see that in Rambam's time, the non-Jews preferred to eat kosher, shechted meat. They even preferred shoes made of leather from kosher animals. Therefore it is misleading to sell non-kosher meat to a non-Jew as if it was kosher. A non-Jew from Rambam's time will welcome the EU legislation because he or she will know that meat which is not pre-stunned is of a superior quality. The animal is more likely to be healthy, and the killing process improves not only the flavour of the meat, but even the quality of the leather.
Now - if we can just begin a campaign to teach the non-Jews the value of kosher meat...