Should I exercise my call option or sell it?
Before expiry, selling usually brings more than exercising, because the option's price includes time value that exercising throws away. Exercising pays only the stock's price minus the strike. The exceptions are a wide bid-ask spread with little time value left (the bid can sit below what exercising pays) and a dividend about to be paid, which can make early exercise worth it for a call deep in the money.
Try it: a call with a $50 strike at 30% implied volatility (made-up numbers). Move the stock, the days left and the spread, and compare the two.
Simulated example, priced by the StrikePath engine (Black–Scholes, interest 4.3% a year). For learning; not advice.
Why selling usually wins
The price of a call on a stock that pays no dividend is never below the stock's price minus the strike's value today, and before expiry it is above it: the extra is time value. Exercising collects only the stock's price minus the strike, so it hands that time value back. Selling collects it, less the half of the spread you give up to sell at the bid.
When exercising can win
When the spread is wide and the time value small, as for a call deep in the money near expiry, the bid can fall below what exercising pays: move the spread up and the days down in the demonstration to see it. A dividend is the other case: the stock's price drops by about the dividend when it goes ex-dividend, and only shareholders receive it, not call holders. For a call deep in the money whose time value is smaller than the dividend, exercising the day before can bring more.
What this shows, and what it doesn't
One contract, model prices, no fees and no dividends, and the shares assumed sold at their price as soon as they arrive. It shows the trade-off, not what to do with your own option.