I have an 12.9 (1st Gen) and had a 9.7, now a 10.5
The 10.5 is really much better for note taking when compared to the 9.7: pencil is serious quicker (delay), friction is a tad better, screen is a little bit wider, making it easier to write sentences, brightness of the screen is much better. I can't really put one big reason, but all in all it really surprised me.
It's not the reason I updated, but it was a nice bonus.
If you don't have the money or are not willing to spend it, get a used/refurbished 9.7. there is no shame in either, I'm a mad idiot spending so much replacing a perfect device for something a little bit better, but I gave the 9.7 to my father, his iPad 4 was getting less and he uses it so much).
A few examples how I use my ipads.
At my desk.
I have the 12.9 in a wooden stand (yohann.com, expensive, but nice) with a keyboard (k380 Logitech, small but good, not to expensive, does things the magic keyboard can't like switch quickly between three devices, so I can wake, unlock & work on my 12.9, 10.5 and iphone without lifting a finger from my keyboard)
The 10.5 is flat on my desk in portrait mode.
This is when I type in one Docx, PDF expert for read/reference in a second on the 12.9 in split screen.
I have Nebo on the 10.5 for notes/todo's, etc.
Like this, not my desk my iPP10 is flat
When with a client.
12.9 flat on the table, pencil for annotating PDF's / writing notes.
10.5 is in my bag or it lays flat in front of my client for reading previous documents/examples.
When in the train/bus/metro/being driven/passenger
12.9 in portrait for reading law textbooks, annotating PDF's.
If it's very crowed I use the 10.5 for reading, but that is less convenient.
In college
When I'm at college I have the 12.9 for taking notes and annotating the spread sheets and the 10.5 as a law text reference books with about 5-10 tabs open in Safari, one for each specific law text that is being used.
Bot flat at a (folding) desk.
Luckily my auditoriums are usually a bit les crowded and I can have 2/3 folding desks for all my stuff.
Other uses or places like bed/couch/Lamzac/hammock
The 12.9 is brilliant for comics (pity I hardly ever read comics), reading newspapers in their respective apps gives a bit "for old times sake" feeling (it's a copy of the paper version) also really nice are magazines. It's unbelievable we liked to do that on a 9.7 iPad, the 12.9 is so much better at this.
The 10.5 is really nice for reading in bed, especially ePub formats and the likes, they scale much better. (You shouldn't be reading in bed, get some rest and performed the next day better/more efficient!)