The 3G operates like a cell phone. You can get a connection to download or browse almost anywhere in the world. The wifi works in hotspots, or your home if you have a wireless network. Both connect to a computer to download documents.
There are significant improvements to the newest Kindle (available Aug 27) which change the comparison to the Nook.
Kindle
sharpest screen in town
holds 3500 books
battery life of a month (without wireless turned on, 2 weeks with wireless turned on)
Even faster page turning (it was already faster than the Nook)
Lightest e-reader at 8 point something ounces
can navigate, enlarge, decrease PDF's
text to voice enabled books
has a new web browser
each kindle has its own unique email address where you can mail yourself documents
3G wireless works all over the world
Nook
has a screen sharpness equal to the last Kindle
holds 1500 books
battery life 10 days (without wireless on, half that with wireless on)
replaceable battery
lag time associated with turning on the device and page turning
color screen is for navigating through menus only, not for reading and visibly refreshes itself repeatedly until it 'sleeps'
can read library books on it (only epub - and like regular books, you have to wait until one is available)
Downloading books to your device (either one) is simple and even if you lose the device, the books you purchase will always be available on your account, at B&N or
Amazon so if you buy another, your stuff purchased is all there.
My suggestion is this: Go to both B&N and Amazon and do searches for e-books on the titles and kinds of books you buy. See which one has the better selection. Both carry bestsellers, etc. I love travel books and I found Amazon had more books of the type I was likely to purchase.