Obviously you shouldn’t only use Japanese the Manga Way, just as you shouldn’t use any single source. That’s why I recommend following up JtMW with Genki’s massive amount of practice exercises (which is where Genki shines)- if you encounter anything that JtMW doesn’t cover, you’ll have Genki on hand. But when you are a beginner in grammar, and have limited time, you have to pick and choose, and my post was about picking, choosing, and dividing up your time.
As far as the scope, I’ve learned far more from JtMW than Genki, as far as grammar goes. Admittedly, this is only Genki I I’m comparing it to- I never made it to Genki II.
A good example is が，は、and を. I don’t have Genki on hand at the moment but I remember it’s coverage of these particles being pretty basic and to the point- like, maybe a page each. The JtMW chapters on them covered around 20 pages (admittedly, these pages are less efficiently laid out than Genki, but still). I came out of them with a much better understanding of their use than I did with all my time using Genki. I was always fuzzy about the difference between はand が in particular, and I came out of JtMW with a better understanding of how they differ, when to use them, and how to pick them out in complex sentences.
Part of the reason I like JtMW is because it is organized based on sentence structure, building up to more and more complex sentences. It starts with the basic types of sentences and works up. While Genki… I’ll be honest. I have no idea what it’s organization is going for. It feels like random pieces of knowledge thrown here and there.
Sorry for the overly long post just barely related to the main topic, it’s just that I spent years trying to use Genki as a primary resource and hitting my head against a wall (It was my school textbook- I didn’t do terribly well in school.). I’m finally making progress in grammar because, to be blunt, I stopped using it.