I think that some people equate handsome with a more masculine looking male face and cute as somewhere between masculine and feminine.
And then there is the handsome women, also normally seen to have stronger features than what may be considered as pretty.
Masculine features are more robust features and indicate higher levels of testosterone, but also relate to lower immunity to disease. They make people look much older when they are younger than those that do not have those features. The baby face as opposed to the mature face.
Science provides evidence that testosterone levels have fallen on average in men in the United States.
It becomes more noticable if you look at the pictures of elementary school age kids from the early 1900's and compare them to elementary school age pictures today. There facial features make them look like little adults compared to the pictures of elementary children today.
It is also evident in the facial features of movie stars before the 1960's. After that if you look at movies and old TV shows from then until now you can see a noticeable change in facial features.
That's in America though, I have no idea if it is changing in other cultures.
The interesting question becomes why. A person doesn't make themselves have the strong facial features that may be considered handsome, they are born with the propensity for those features.
In general, though, the features may be related to testosterone; there are so many factors in the modern environment that may influence it. Some theorize that the "pill" influences a woman to desire a less masculine man with lower levels of testosterone; could that be part of it? I'm not sure.
So is the "Marlboro Man" gone? No, but he might not be as evident as before.
And I know, it is much more complicated than that; most of what I present here is anecdotal in nature, and a matter of personal preference, but I think this might be part of it.
Sorry, if I elaborated too much.