Is Ano Natsu de Matteru a romantic comedy or a lighthearted romance?
Overall, I think the anime was expertly executed. I am struggling to identify a romantic comedy equally good. [...]
(He then identifies Nodame Cantabile as a strong contender but feels its focus was more or less elsewhere.)
I've been thinking about this, and I'm not sure that Ano Natsu is really a romantic comedy; it's a romance, but not so much a comedy in the way that, say, Nodame Cantabile is.
Ano Natsu is certainly a lighthearted romance where amusing and funny things happen (mostly because of Remon), but I'm hard put to think of actual comedy that happens in the show. In fact it's strikingly missing many or all of the painful stock comedy elements you find in ordinary romantic comedies. I think it's a 'romantic comedy' only by default, because we don't have a better name for a lighthearted, amusing romance that doesn't focus on melodrama or straightforward love.
(Since I don't watch mainstream American TV or movies, I'm actually stretching my mind all the way back to memories of to Shakespeare's romantic comedies as my basis for comparison here.)
Nodame Cantabile makes an especially good comparison for this because it's clear that Nodame has significant comedy elements that are played that way deliberately. For example, Milch spends a lot of the time being a comedic character that we are supposed to laugh at, we have several secondary characters as exaggerated comedic foils (even if they develop their own depths in time), and we have the ongoing saga of Nodame's messiness versus Chiaki's obsessive neatness. Fundamentally all of these are played for laughs in a way that I don't think any element of Ano Natsu is. Even Remon yanking people's chains has an edge; it's funny because she's making people be truthful (even if other characters don't realize it).
(The closest element in Ano Natsu is perhaps what's up with Mio's odd behavior, but there is very little actual comedy with that and it becomes a strong dramatic element almost the moment it's really focused on.)
PS: this entry is brought to you by insomnia; despite the posting time most of it was written at 4am.