I have a Nook Color I got the month they came out. I love it. If Nook is what she wants that is what I would get her.
Both have a large selection of free books. But you wont usually find the best sellers for free. Both have systems to borrow from libraries, but not all libraries have the system for either or both.
Nook-One hour in store reading of most titles each day. I enjoy this. I can take my Nook to the store and start reading to see if I want to buy something. Or just sit and enjoy a coffee and read.
Free Nook Fridays. A new free book every Friday. Various titles, sometimes best sellers, sometimes new authors.
Kindle-You can borrow one free book a month if you are also an
Amazon Prime member. Amazon Prime is $80 a year, so IMO, not worth it just for one book a month.
Kindle Direct Publishing is more author friendly than Nook's direct publishing service, so there are more books that are free on Kindle, but again, these are all self published.
With the free books you have to be careful you know what you are downloading. Because with both Nook and Kindle there are a lot of self published books that might not have any reviews or a good overview. There are a few books and short stories I have started to read that I wish I had not. There are also many free books that I read and loved.