Please someone correct me if I get anything wrong.
For an Euro option, if it expires past the ex-dividend date, and the dividends is higher than expected, the value of the call would decrease because we cannot exercise to obtain the underlying asset’s cash flows.
Other things equal, an American call should have a higher value than an Euro call because of the free right to exercise at anytime.
For an American option, if the dividends increase (i.e higher than expected), the value of the call should also increase because we can exercise at anytime. Honestly, I’m not sure if it should increase or stays the same here. Either way, it would have a higher price than an Euro call.