I've had the Nexus 7 (2012), the Nexus 7 (2013) and an iPad (Gen 3) prior to getting the Nexus 9 a week or so ago. The 9 is a nice tablet, and while I hear some comments about build quality, it's a nice tablet. No light bleed and no flex on the back of the case. But, also, all my tablets end up in slim cases like the Poetic for the Nexus 7, so I anticipate the 9 will be, too.
At first I was a bit annoyed at the subtle placement of the power and volume buttons, but with Lollipop a double tap on screen turns the device on,, so that's not much of an issue.
With a 7 and a 9 on the table available to her, my wife favors the 9 for everything except popping into to her purse for waiting at medical appointments, riding the bus, etc. She says that once she has a good case, she'll take the 9 since it fits in her purse. The larger screen real estate really is nice.
My iPad was a gift, and it's larger screen is nice for things like sharing photos and reading long documents or magazines. But I find iOS immensely frustrating, from minor-but-not-really-that-minor annoyances like no back button and many fewer options for sharing to applications. So a larger screen Android tablet is really a sweet thing to contemplate....
So far few problems with apps on Lollipop and very excited to see how this new OS will grow and mature.