I read the series up until the big storytelling change (won't spoil it, though it's not a big deal), and then I saw some of the untranslated chapters after that. I really liked what I read.
The way the OP compares it Yotsubato works well. We might not see Koiwai struggling to figure out how to make ends meet or calling his mother for advice on what to do, but we can probably assume he would have to do that from time to time. Usagi Drop shows us those kinds of moments, and does it well. It's interesting to watch the parental relationship build, especially with the scenes of how difficult building that relationship really is. It's got a good mix of realism mixed with comic book melodrama and, of course, lots of cuteness.
I hadn't heard about the anime adaptation, so thanks for mentioning it here! I'll definitely be checking it out.