From what I've seen, Japanese dramas depict romantic relationships in a very platonic way. One of the main reasons that happens I think is because Japanese dramas tend to focus more on the comedy than the romance part and even so, their main premise centers around two people who grow as friends and eventually, start to develop feelings for each other... feelings that most of the time are portrayed as innocent and naive. Well, I personally love jdramas because they are so unique, even though they don't take romantic relationships as serious.
On the other hand, Korean dramas mostly focus on the romance and they contain so many lovey-dovey moments, but I find that even them portray love in a very sweet, innocent way, even though we're talking about adults, like @Bonny said. But I do think kdramas are the best when it comes to romance and to be honest, I'm actually more interested in a romantic relationship rather than physical ones, so it doesn't really bother me.
And about Chinese and Taiwanese dramas... I still don't know what to think about them, but I believe they're the closest to depicting both of the romantic and physical part of a relationship. Though, sometimes, they're very similar to Korean dramas in their view on romance.
Now, if I were to compare Asian series to the American ones, for example, I'd much prefer the Asian ones just because I find that most of the American movies depict love in such a superficial way and they mainly focus on the pyshical aspect of a relationship. So no matter how much someone complaines about the lack in action in Asian dramas, I'd rather watch them than the mindless love that we usually see on tv.