It'll be a while before I get around to reading and watching the Japanese versions of LOTR, but I'll certainly let you know what I think. It goes without saying that the dubbed version will probably give a fuller impression of the dialogue, but as you know, the "equivalent" expressions in different languages often convey different impressions. In glancing through "The Hobbit" in Japanese, though, I did notice that an effort was made to rhyme the songs, and that Gollum was called Gokuri, which is the Japanese expression for a gulping sound...nice touch.
I fear the "All Your Base Are Belong To Us" effect.
That would only happen if the Japanese were translating into English...and then it would be almost guaranteed :-) One concern I might have is that the subtitle translators here seemingly work at times from the video and not the script, as I have encountered the occasional mistranslation (when I'm paying attention) that without question came from a misunderstanding of the spoken word.
Does New Line have it translated it and dubbed around the world, or do third parties in each country do that? - Is there an "approval" process with New Line to officially sanction the translation?
The subtitle translation for LOTR was done by Natsuko Toda, a name you would probably recognize if you watched a few American movies here as she does the subtitles for lots of the big hits (she also did Harry Potter). She was helped by Akiko Tanaka, who is the translator given the responsibility of polishing up and correcting Teiji Seta's 1960s translation -- apparently there were some inconsistencies in personal/place name renderings into Japanese as well as some questionable spots. I would guess that the dubbing was done in Japan by a local company hired by New Line. I'm sure this is all more information than you need or want, right?
If you're curious to see which Tolkien books have been published in Japan and what their covers look like, you might take a peep at this page; don't worry...it's in English.
Oh, BTW, "The Hobbit" (two volumes in Japanese paperback) is now ranked No. 24 and 26 on Amazon Japan...Bilbo lives!