I'm new here and I didn't watch many so I'd like to here your opinion about this.

What usual differences did you notice between Japanese and Korean drama or movies?

(Compare those in terms of story, actors, music, camerawork, surprise effects, endings,...). 

I don't often enjoy japanese fiction (movie, drama, specials etc.)...how to say...I find it too psychological, metaphysical, it's always very deep but emotions are not intensely displayed. With J-fiction it's all in the dialogues and story, not the behavior. I watch dramas to first be entertained not to reflect so I don't usually enjoy J fictions. I still have some I like though.
Korean fiction is more superficial in a sense, the interactions between characters are more passionate, whether it's hate or love, it's not all in what they say but also in what they do and how they do it, it's raw instinct. But K-drama really suck at endings, 9/10 times the ending is disappointing or unsatisfying. Also, sometimes the story makes a total 360 turn, in J-drama the plot is more consistent.
I prefer K-fiction music and surprise effects, it's more diverse.
As for actors I don't see any specific differences.
An image would be: to me J-dramas are cold, K-dramas are warm. So I usually enjoy the latter more.

With dramas, I think the biggest difference is production. Korean dramas are shot more lavishly while Japanese dramas tend to have less gloss and special effects. Also, Korea tends to churn out more romance and skinship while Japan really loves thier mystery and detective dramas.

With movies, Japan does better with production and visuals. Japan has many different styles and genres, from outright insanely crazy weird stuff to deeply introspective drama. Korean movies overall seem rushed to me. The pacing is similar to dramas and since it's only two hours, many times I tend to feel like story parts are missing. Not all the time, mind you, but these are just some things that I have noticed over the years.

Both countries produce great dramas and movies, but yes you can tell a difference. After you watch a few of each you'll see what I mean. :p
I've watched a fair amount of both and I don't fully agree with KMR in the sense of the display of emotions in Japanese dramas. I feel it's unfair to say that Japanese dramas lack emotion/passion. I would say that it's all dependant on the character portrayal and the cultural differences between Korea and Japan.

Ill put it this way. I've noticed that the Japanese are more of the opinion; keep your emotions to yourself (It's all about propriety) so if the drama is portraying your average citizen they would lack the animated characters you find in the average Korean Rom-Com. On the other hand if a Japanese drama is portraying High schoolers or a non-average person, then you will find a lively atmosphere filled with different emotions.  Koreans are more of the types to scream out their emotions... in fact i noticed that they encourage this a lot. They just let it all out, regardless of the consequences, which to me is a lot healthier. Most dramas whether it be rom com to melo show characters that will express their emotions to the fullest. So if they are crying in a melo, they will all out drop to their knees and start thumping their chests to show that pain.
Whereas in a Japanese drama it would depend on the character, he could be the type to cry and scream (passionate non-average citizen) or he might be the type to silently take it in (shed a few tears) and show his pain in his future choices/actions, maybe explode in the finale. In this sense the Japanese explore the psychological effects of the situation at hand. 

The Japanese also have a specific type of acting/genre where they have this tendency to over-exaggerate in a way that they literally act like anime. This type of characterisation is either liked or disliked. there is no grey area. 

In other words it all depends on the choice you make when choosing a drama to watch. With Korean dramas they have a good range but it doesn't vary. They follow a strict guideline for character generation (creation) and drama scripts and story lines... You have Melo, Revenge/Action, Family, Historical and Rom-com. You will find that once you've watched the classics then you have watched all Kdramas out there.
Whereas the Japanese have a wide variety of acting types within the genre (different characters and their portrayals), they could have a thought provoking script filled with realism or just a plain stupid light dramas. i.e: a Police drama can be psychological and thought invoking, dumb/light with anime style characters or a quirky main character surrounded by your average citizens. Whereas a Korean Police drama will either be Action revenge or Action Revenge with a bit of comedy on the side.

As for the visuals, I have nothing to add to what Cherry Bunny has stated. Sometimes I wish the Japanese would be more like the Koreans in that department. I would say Ive seen them do it once. And that was in the drama Rich Man Poor Woman. It gave off Korean Drama vibes and to me it made a big difference.  If I was to say which I prefer. In the long run I prefer Japanese drama because they are a lot more diverse and I like things that make me think. But in the short term I love Korean dramas and the way they set everything so lavishly. However it gets boring if your watching the same thing over and over... I feel that sometimes their dramas are too 2D there's no 3rd dimension to their characters. Most of the time they are shallow. But ofcourse you have exceptions such as Misaeng, Can You Hear My Heart or Two Weeks. 

So I tend to switch from country to country. Japan, Taiwan, Thailand and Korea all have their own styles which to me is incomparable. Therefore I don't really have one that I like more than the other!