They are both correct!
When people resemble each other, it means mostly they are similar in looks and appearance,but it could also refer to other characteristic such as manners, habits etc....
When you say that people look alike, it means they resemble each other in looks and appearance in particular.
If you don't use the verb 'look' and use instead ' to be' :
"They are much alike".
Here it could refer to any kind of resemblance not necessarily to physical appearance.