For non-dividend paying stock, value of call option is same for European option as well as American options- logic being, if you are not going to get anything extra by exercising early, then why would you pay more. But isn’t it true that chances of an American option could end up in more payoff than European. If any day when the stock is higher than strike price, you will exercise the option. So why should the value be same.
If you’re smart, you will not exercise the option; you’ll sell the option.
If you exercise the option, you get the intrinsic value; if you sell the option, you get the intrinsic value plus the time value, and the time value is positive.
This is true for American options and European options.