Actually, I'm pretty sure the invincibility time is the same. I've played both versions multiple times, and they certainly felt the same. It's just that in the Japanese game, it's really no big deal if you get hit three times in quick succession, while in the US version, that much is often enough to kill you.
That's the biggest difference between the two. In the Japanese version, it usually takes 10-20 hits to die, while in the US version, it's 3-5. I don't blame them for wanting to tweak the difficulty, because the original is honestly quite a breeze, but IMHO, they screwed the balance up. When you play the original, you get the sense that being able to survive a rapid succession of hits is a very intentional part of the game design. If Working Designs had to adjust things, they should have either also extended the invincibility time or reduced the hits-to-death to something more moderate, like 5-10.
Popful Mail US isn't really hard, but it's kind of cheap. You need to save and reload all the time, which is tedious, and the bosses throw the difficulty progression of the game all out-of-whack. I think the Wood Golem boss of the first world is harder than any of the final bosses, and so is that one two-faced guy who bounces around. In Popful Mail JP, those guys do far less damage, and even if it's easy, the progression feels very balanced and reasonable.
Great translation, though.