Which kindle? Kindle Fire, or one of the e-ink gray scale screens.
Generally speaking an iPad is more capable in every way than a Kindle (faster, better screen, more apps), and you can install the Kindle App on the iPad, along with the Nook App (if you happen to like Barnes and Noble books over Amazon), and of course the is Apple's iBooks app, and half a dozen other ebook apps available for the iPad.
The Kindle weighs less than the full sized iPad. However, the new iPad mini is much lighter, and more in line with the size of the Kindle or Nook devices.
If you are talking about one of the e-ink Kindles, then that will last much longer on a single charge, but mostly they are best for reading books, and are rather limited in what else they can do. But if reading books is your primary desire, then a Kindle (or Nook) with e-ink display just might be what you want.
If I were you I would visit an Apple Store and play with an iPad, an iPad mini (or another store that carries Apple's iPads), then visit a Barnes and Noble to look at the Nook, and finally find a store that carries the Kindle (Staples I think carries Kindles). Actually play with each of the devices and then decide. Anything we say in these forums is not going to be a good as touching the devices yourself.