@Xenokitten 

I so agree with you about The Fault in Our Stars! I saw it and I liked it, but it didn't move me in a fundamental way like a few Asian movies that I've seen. It was an entertaining, romantic film that I was able to escape into despite the cancer. The cancer didn't take centre stage as it probably would have in an Asian drama or movie.

Ironically, you can say this is what I liked about the film ... and what I'd criticize about the film. Let me try to explain. 

Since I started watching Asian dramas & movies, one of the things I came to appreciate more about Western cinema & TV is that they don't demand too much emotionally from the viewer. They provide entertainment without a lot negative emotional upheaval. Even when someone dies or gets sick, the tone is still optimistic and hopeful, and the protagonist always 'wins', which can be uplifting when we know in real life the opposite is often true. I've seen a lot of viewers give this as one of the reasons why they like Asian cinema better (because it's more realistic), but I personally appreciate the message that you can do it, you can win. You can be a superhero and fight for world peace, you can beat cancer, you can catch the bad guy and still come out alive. I like this positive messaging. 

Another great thing about Western cinema is that when creators have a mind to Western shows and movies can be very moving, but they still kind of leave you in a buoyant mood.

On the other hand Asian cinema is so filled with the deepness and meaningfulness that we often experience in real life. This is certainly a good thing, but it also comes with a downside, that things can feel too real, too depressing, too pessimistic and too emotionally demanding. I want to be entertained and moved, without such emotional overload.

I prefer poignant stories that touch me gently in the moment, but allows me to move on with my life without feeling burdened with negative emotions (sadness, melancholy, depression etc) once the credits roll. Some people have explained to me that a drama which allows them to cry their hearts out is very therapeutic for them. I find this fascinating because it is the complete opposite for me. I'd rather laugh & smile, than cry (because I think life gives us enough reason to cry, even in the best of circumstances). I'm quite sensitive ... I wouldn't go as far as to say I'm hypersensitive, but I'm empathetic and I tend to internalize a lot of what I see in a movie or drama. If there's a lot of suffering and weeping and moaning and gnashing of teeth, I get overwhelmed ... I start to fret about all the injustices of life, why bad things happen to good people and so on. I don't watch TV shows after a tiring and eventful day to be burdened with the same things I see and hear on the evening news. Sometimes if the show was really hardcore with the melodrama, it can take days for me to recover to my normal self. So for me it's not theraupetic at all, but rather burdensome.

I want a balance of real life and the potential to escape into the story. Not pure fantasy, but not so starkly realistic that you can't escape away from all the sadness and pessimism life has to offer. In general I sometimes feel Asian dramas focus too much on the tragedies of life (esp true for Japanese dramas, in my experience) ... while Western cinema & TV give us an outlet.

Having said that I've watched a few wonderfully moving without being emotionally burdensome films (I deliberately stay away from emotionally burdensome dramas) from Asia and I haven't been able to find their Western counterparts. So what I've said is not really a complaint against Asian dramas/cinema, but more of an observation of how the two regions are sort of perfect complements of each other, in some sort of strange, inexplicable way.
Asian > Western 

Deal with it :)
Since I've never really watched much Western TV, except for movies it's hard for me to compare. I started watching K-dramas while cleaning.. my girls would have it on. I liked that fact that they were so immersed in another culture. For me that was probably the draw, the cultural aspect. I like the tradition and sense of family in most of the dramas. And I enjoy l other languages so it's been fun to try to learn some common phrases. The patriarchy social system in Korea is interesting compared to the Western version of it. All that set aside, you can't beat the humor in some of the dramas.. Like I said feel like I can't give a fair evaluation since I've never really watched much Western TV... but I don't have time to do both..so for now I will stick to the Kdramas and hope to visit Korea soon to see some of the places and meet the people. 
Although I do watch some Western shows (The Big Bang Theory, Game of Thrones, Once Upon A Time, Suits) and love them, I still prefer Asian dramas because, personally, I feel at home while watching them. I can't feel that "personal attachment" with the aforementioned shows. (Though it's actually weird because GOT and OUAT aren't exactly shows which depict lives of people from the West. Idk with myself. orz)
I put it like this. I like apples, now I prefer oranges. Although I know I'm missing out on some really nice apples.
Sometimes I'll try an apple again. If it;s a small apple I'll eat it all. If it's a big one, I'm inclined to take a bite or two, and think, that  
I would prefer an orange instead.
And nobody knows what the fu I'm on about :)
But to answer the question specifically. What I think american dramas are missing is
(1) a lackof earnestness
(2) a willingness to mix up genres within an episode
(3) knowing when to stop a drama
(4) great eating scenes