What is the meaning of face value of a stock? And if a share has a face value of 10 and another has face value 1 then does it mean that the former is a better stock?

Face value doesn’t predict if a company is better than other.

At the starting of the company, face value is decided to divide the shares among the promoter and the partners.

Suppose, they start the company with 1,00,000(seed fund).

If they want to divide company into 1,00,000 shares, then the face value will be 1.

If they want to start with 20,000 shares, then face value will be 5.

So, basically it depends on the seed fund and the no of shares.

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Basically how does the face value of a stock affect it or in which case it matters? Does it affect the dividends anyway?

I don’t think so. It’s up to the company how much dividend they want to pay out of the profit they earn.
Note : Companies with major holdings by government will pay more dividend.