Neither Capitalism or Socialism are intrinsically correct. They are both just ways of organising societies, with associated outcomes.
However, some in our society have a habit of viewing things in very black and white terms, as binary situations. The vast majority of us actually believe we're better off with some form of mixed economy, and we just argue about what the right balance is. So let's deal with the errors behind the black and white assumptions, and work out what the really fundamental difference actually is.
Those with a distaste for capitalism will discuss it in extreme terms, as if it's a game of Monopoly where the winner takes all. In fairness this is the logical conclusion of where unfettered capitalism ends up, but in the UK we don't have unfettered capitalism, we have a mixed economy. We are currently heavily capitalist, but we also have some level of democratic government with taxation, and anti-competition laws with some element of a welfare state. We're currently seeing increasing levels of inequality, but we're not in the absolute final stages of Monopoly yet. We still have the luxury of considering that "dystopian fiction." It hasn't happened, yet.
On the other hand, those with a distaste for Socialism will argue how it supposedly leads to lazyness and eventual collapse, and how it has supposed failed everywhere that it's been tried, They will point to the USSR, while ignoring the massive success of the NHS and the fact that every public industry which has been privatised in the UK, was turning a profit before doing so.
If we're going to get to a reasonably objective truth, we need to define the terms we're using. For the sake of this argument I'm going to use the following definitions.
For clarity I will also define Communism as a classless society in which people work "from those according to their ability to those according to their needs". I'm not discussing Communism here. At All. It's an entirely different thing.
In both Capitalism and Socialism, individuals gain wealth by providing services for other people who have something that they want. For the sake of simplicity let's call that "money". There is nothing in either definition above which places an intrinsic limit on the amount of money that anyone can earn.
If you switch from a capitalist to a socialist system, that doesn't change. The incentive is the same. Money. And maybe having your boss praise you or shout at you, depending on their managerial style. But ultimately, in a Socialist or a Capitalist system, the basic incentive is the same; Money.
As such there is no inherent reason why a socialist company will fail, where a capitalist company will succeed. The incentives are the same.
Now some might suggest that capitalism promotes innovation where socialism does not, but if you look at the definitions of both above, there is nothing inherent in them which makes this the case. Most innovation in capitalist societies is actually found within universities, government institutions, or within major corporations where creative people are simply paid to be creative.
It's implicit in the definitions. It's who you work for. Nothing else.
Under Capitalism people work for whoever has the money to pay them. The greater the inequality in society, the larger the extent to which society is simply organised around fulfilling the needs of the richest. The lower the inequality, the more people are working for each other, and not just the richest. The level of inequality in a capitalist system is a big deal.
Under Socialism, society is organised such that people work for the benefit of society as a whole. Healthcare, transport, housing, art, public spaces are created for everyone.
How we create money, and what we use it for is also a very big deal.
And let's not forget that all important point I came in on. Most of us currently believe we're better off with some form of mixed economy, and it's actually just a case of how we choose to balance the two. Even the current UK Labour Party Manifesto, which is to the left of the UK Overton Window, leaves the majority of the economy in private hands, no matter how "socialist" they claim to be.