>in Europe at best you'll receive a few hundred euros a month in disability pay.
Uhmm, no, at least not here in Germany. The amount on compensation is related to the severity of the injury. For things that heal you will get Schmerzensgeld ("pain" money), as well as compensation for things that broke (e.g. your car or bike in a traffic accident). If the injury takes a while to heal, in which time you're unable to work, you get compensated for that as well. If it's lasting damage, you will get disability money. If you need care/help (from grocery shopping and cooking, to full blown 24/7 nurse care) that is compensated as well, and may amount to tens of thousands of euros per month. If you're permanently unable to work you will get compensated for that in a "reasonable" way (you won't be poor), and the liable party will also have to pay your retirement insurance dues[0]. If you requires changes to your living situation[1], you will get "reasonably" compensated as well. And so on. Basically, every damage that can be monetarily valued or at least estimated will be "reasonably" compensated.
>In US you could sue for millions.
Where you're right is that you won't get rich from such a lawsuit. Regardless, the total amount in compensation you will receive over a life time could as well amount to millions as well. The amounts awarded in the US may seem large sometimes, until you realize that it's a one time thing, and the health and care costs over a lifetime you will incur may still not be covered by that lump sum.
The only thing here in Germany that isn't really direct compensation but "extra" money is the Schmerzensgeld, and that's usually a one time pay of a couple hundred bucks for light injuries up to low six figures for major injuries.
And it might be harder to "fully" win such a lawsuit too, as in Germany you don't have jury trials[2].
[0] Retirement insurance dues may have to be paid even if the injured party was not working yet, e.g. when the person was still in school.
[1] E.g. you need a wheel chair ramp, or move to a wheel chair accessible place, or need to make changes to your bathroom to get in and out of the shower/bathtub. In some cases, defendants were ordered to pay the difference for getting a larger house so family providing some care could move in.
[2] Tho, there are Schöffengerichte, with "regular" people sitting on a panel with a judge, usually 2 regular people and 1 judge in the lower courts. While the judge can be outvoted in theory by the 2 other, the judge is part of the deliberations and therefore has great input into the decision finding.