There's a few things. Obviously the storyline is more compelling and intricate in LV. The overall art direction is also beyond what Park Chan-wook put together in Oldboy. There's actually two versions of the movie. The first is the normal one that you've probably seen. The second is one that was the director's pet project, and his actual intention for the movie. It begins in color, and gradually fades to black & white. It was known as the Fade to White version, if you want to try and find that. It really does an excellent job of highlighting various themes as the plot progresses.
The main reason I prefer LV is something that I'm not sure I can help you to understand that much. The standard English subtitles do a great job of expressing the story, but fail to cover the nuance of the script. When I first watched it, I felt as though I was watching a thriller. In reality, it is truly a dark comedy. Korean is an incredibly subtle language, and Park Chan-wook wrote a brilliant script with many lines that can have multiple meanings within the context of their scene. It's a very clever and funny movie, however that part of it is almost entirely lost in translation. It wasn't until I was able to watch it without subtitles that I really felt that I was able to understand and appreciate it.
This all isn't to take anything away from Oldboy, btw. I still love that movie, but it's more straightforward in a what you see is what you get kind of way. Oldboy is a great thriller with a fantastic twist at the end, but compared to LV it simply feels like it's lacking a dimension.
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