Again, Mini vs. Air

Hey guys,

after a frustrating week with the Dell Venue 8 Pro (which I'm sending back for a full refund), I'm considering getting an iPad. The current generation is starting to pop up in one of the refurb stores I visit and I figured now would be a great time to get one.

I use a Mac Mini as my main (and currently only) computing device and I'm torn between getting an iPad Mini Retina, or an iPad Air. The iPad Mini only saves me 40 € over the Air, so price isn't as much of a factor as it would be.

What other advantages does the Mini have over the Air?

I like that it's not as cumbersome and taking it out seems more casual, but other than that?
It's not like you could carry either without a bag.

I'm using the iPad as a complementary device to give music lessons, take with me when I study in the library, read sheet music, read and write emails, use reminders and the apple calendar etc.

Reading sheet music alone should be enough of a reason to get the Air, but maybe I'm overlooking major advantages of the Mini?