Depends on what you mean by inequality. I'm European. Belgian to be exact. And we do have inequality. A doctor or a CEO of a company makes much more than somebody working a cash register. In other words there's an incentive to try to do well in live. If you want to afford that 2nd house in Toscana. You can even be a billionaire. The difference lies in to what level you are allowed to sink by society. Here some things are considered basic rights. Housing, food, education for your children, healthcare are more or less guaranteed.
Capitalism as exists in the US, ( a comparison I'm able to make since my wife is American) is more of the variety of every man for himself. This creates conditions that are unheard of here. I have a good life work balance In total guaranteeing at least 30 paid days of per year not counting overtime. Americans are totally dependant on their employers willingness to be off.
There's no concept of sick days either. You sick you stay home. I have healthcare that I can afford and that's guaranteed. My daughter will be able to go to college without taking out loans. Etc.,etc.
In short people, a few exceptions notwithstanding, mostly in the big cities and being illegals or people whose life fell apart to such an extent that they don't want or can't be in the system. Will have a certain base standard of living.
When I visited my wife's family both in NY and Florida. I was appalled by the struggles of them although they are by no means poor. And even more shocked by the abject poverty I saw in general. A poverty that is much much more rare here.
And before you or anybody else says it. Yes my tax rate is much higher here. On the other hand so is my standard of living IMO. I'm not expected to work from the cradle to the grave here, I can be sick without fearing for my job, my child can have a decent education without indebting herself. And I can do all this and still afford a house, two cars, at least one vacation a year, and peace of mind. Precisely because here, inequality is accepted but also has limitations put on it.