Both are very 2 different devices. Both are capable on its own. Either one you buy, you wont be disappointed.
The above post that says, almost no data transfer from your PC is completely wrong. I use Android, iOS and Windows. Whatever I do in one, I am able to do in others. Why only yesterday I copied a tonne of my photos and wallpapers to my iphone 6 plus using the itunes Photo sync from folders feature, My music through itunes (just drag and drop if you click manage music manually or independently or something), Around 35 GB of mp4/mkv movie and tv shows via VidOn player app file transfer, My PDF/CBR files through CloudReader file transfer feature. I really dont see what is so different or ghastly about these.
One needs to use Windows File explorer(This is available in any PC) and use few clicks there or use iTunes(This is not.
So if you want to do something you NEED iTunes) and use few clicks there. You dont miss out on anything. I bought my iphone after using iPad and iPod Touch for over a year. And i wanted to make sure that I would be able to do everything I do on my Note 3 on the iOS. and It does. Now if you dont want iTunes look Android only. I feel 2 plus points to Andorid for an average user is, Its just plug and play and home screeen widgets.
iOS has nothing to match for that.
Coming to USB OTG, Android still is the king. But I been using Android high end or most community support devices for last 5+ years. Still to use that feature. No idea why. If thats an important feature you require, look to Android only. Come to think of it, I use streaming and High capacity mem card to supplement. Perhaps thats why.
Whatever fun stuff I do with my Note 3 I am able to do with my iphone 6 plus. As i am using both of em for the last week.
.
So there you go.
My current device list is Galaxy Nexus s(Rooted), Galaxy Grand 2(Rooted), Note 3 N9005(Multi X ROM), iPad Air(JB), iPod Touch(JB)(which I am gonna sell), iPhone 5S 32GB, iPhone plus 128GB(v8.1), Dell Venue Pro 11, Aspire S7. My main requirement for any new device in my list is it should be able to do everything I do in any of my already owned devices.
Between iPad and Nexus 9, I would pick any. Both are extremely well built and feature rich device. Both are toe to toe IMO. But I do feel the display and Touch of the Air 2 is extremely good. Yet to see the Nexus 9 in person. Unless you have any apps that is not available in one of the eco system, budget is the only thing that holds you back.