I prefer the use of Japanese, I find it flows well with breathing, execution of technique and mindset.
I once had a sensei who was Russian, every technique - he named in English, Japanese and Russian
As I see it, the main upside of teaching Japanese terminology in training is, as has been mentioned earlier in the thread, to make it easier for people that don't share nationalities to still understand one another without creating the need for someone who doesn't speak very good English to learn the English equivalent for a bunch of techniques.
This is useful not only when going from school to school within the same martial art, but also across different MAs with the same background (in this case, Japanese); I haven't practiced Karate for a moment of my life, but if someone talks about gyaku geri (no clue if this actually exists) I can get an idea of what the technique entails, being that I have an understanding for what the individual words mean.
That said, having the instructor say "Alright, we're gonna drill Kote Gaeshi!" followed by half the class going "Uh, is that the one where you twist the...?" is just annoying, and can hamper the progress of otherwise talented individuals, so a degree of restraint and understanding is essential on the part of the instructor.
Every activity has a language that serves as its intentional medium. If you watch a tennis tournament, every player, no matter what country they're from, knows what "fifteen", "thirty", "forty", "fault", "let", and "out" mean. When I was studying classical music in college, the language was Italian. Everyone who reads a score, no matter what country they're from, knows what allegro moderato means, and knows where to go when the music says D.C. al Fine. It only makes sense that we have such an international medium for budo, and it only makes sense that this medium be Japanese.
Check out this Cornish wrestling vid (is that uke goshi at 5.22?)
or Breton wrestling
The only parts of judo that are peculliar to Japanese culture is the terminology and the bowing
As far as the technique itself goes, well, comparing that Cornish Wrestling video to a video of Kodokan Judoka speaks for itself. To quote an instructor I saw somewhere,"If all you want to do is work hard, you can put on roller skates and stumble around if you want - but this is all about building a Ferrari."
Would you say Mexican and French cuisine are the same because they are both food?