Japanese text requires fewer characters than languages using the Roman alphabet, so it requires fewer text boxes/screens. The Japanese version is often faster for that reason alone, and can be a big time save in text-heavy games. There can also be differences in how the game plays, particularly in older games, where various changes were made for the different audience according to the whims of the localizers.
That said, it's not universally the case that the Japanese version is more popular—see Faxanadu, for example. It really depends on how a particular speedrunning community develops.
Sometimes the JP version is the first to come out and very obviously the one with the most glitches, hence why you would wanna run it. Often it's because faster text scrolling / less text, or in a few cases shorter audio.
The exclusivity of glitches is a relict from the past, which rarely applies to modern speedgames at this point (unless console games). However, the language is sometimes faster.
The reason for picking a specific language for a speedrun usually boils down to this: -The text is faster, therefore, the run is faster (fewer textboxes for example) -The version has specific glitches. Most of the time in the modern day and age, this becomes very rare due to games being released roughly at the same time. But this is very prominent in older games. -It's funny
Sometimes speedrunners might choose other languages than Japanese. There are several examples from GDQ (I forgot which games) where the runners chose German or French, because they were faster than all other options.
Twilight Princess in german has 1 textboss less for the waterbombs French is faster in Skyrim due to the unskippable parts of dialogs are based on the voice acting speed. And french just happens to be the fastest voice acting. Same goes btw for Deus Ex Human Revolution with french.
For a direct example, Rune Factory 1 on the DS has it's glitched categories run exclusively on the JP version. This is only because of a single but incredibly powerful glitch that was patched out in other releases. The game can be run without it, sure, but it cuts a third off the run's length alone. The sequel also has an exclusive glitch, but it's not as powerful.
I've grown to heavily dislike version exclusive glitches, personally. It just makes the speedgame harder to access for new players, and I'd rather have more runners than a shorter time.
As another example, Disney Tarzan has a japanese version for PS1 that actually has less HP for certain enemies, making it a lot faster to complete the second-to-last level in the game (which forces you to kill several enemies to progress), so it's naturally the preferred version for that console.
[quote=Oreo321]Sometimes speedrunners might choose other languages than Japanese. There are several examples from GDQ (I forgot which games) where the runners chose German or French, because they were faster than all other options.[/quote]
raises hand
My AGDQ run was done in Italian, because fast
Additionally, for some horror games, JP releases are faster because of less onscreen gore (and therefore, less lag).