I'm not some authority, but as a western fan who's been aware of / watching jap wrestling since ~2006, I'd like to throw in my two cents. My friends and I were pretty into the online scenes and had a couple local guys who sold bootleg japanese DVDs. In order in how I would have placed them at the time (2008-ish to 2013-ish)
>NJPW
always felt like the WWE of japan. The biggest company, unassailable. Even during their bad years, they felt head and shoulders above everyone else in terms of popularity.
>DragonGate
I never watched much Dragon Gate, not to my tastes, but the rest of my friends did. From what I saw, they were always doing something and always felt like they had good crowds.
>DDT
can't add much insight on DDT, but they were everywhere, always had someone talking about it.
>NOAH
I was aware of NOAH, and actually probably watched more NOAH than anything else at this time due to ROH, but they never felt like a big deal.
>AJPW
I knew AJPW existed in the past, like with the 90's Misawa matches and all, but I had no idea they were still around. Thinking about it, I wonder if I thought they had closed down after NOAH started.
>everyone else
I was aware of other promotions - BJW and HUSTLE are the two biggest ones I can think of - but they all felt like "Japanese Indies" in comparison
Again, I'm not using any kind of objective measurement, I'm just stating what it felt like back then as a wrestling fan.