But when it comes to night battles, I think that Aoba's the superior one...

You're more naïve than a newborn babe!!! Japan uses 'sweet' for various things, including naïvety; here, Pen says that Aoba is more 'sweet' than a candy apple on a 'related day', a day related to a specific deity, where there are often festivals at shrines/temples that have, amongst other things, food stalls - which is usually the only place that you'd see candy apples in Japan. The word for 'related day' can also refer directly to the festival itself, without referencing the day.

We need to do something about this left-over recording media!