E-ink Kindles such as the Paperwhite use an "experimental" web kit browser similar to the one you have on your KK. As far as I'm concerned, the experiment has failed and the browser is close to worthless. However, you should be able to access the Safari mobile site with it:
http://support.safaribooksonline.com/view?id=1123
In all other respects, the PW2 is a great e-reader and would be my top choice, particularly since you already have a Kindle library. Although I could be wrong, I don't think it's likely that Amazon will re-introduce another large screen e-ink device. They're much more expensive to manufacture and the market demand just doesn't seem to be there now that so many buyers who want large screen devices are opting for multi-purpose tablets.
I do most of my reading on a PW. The lighting and display resolution are great and I think it provides the best reading experience for most ebooks. However, I also have a Nook HD+ 9" tablet which I use for reading PDF's, magazines, online articles, graphic novels and books with photos, maps and illustrations. The added benefit of having a large screen tablet is that it's great for watching videos, checking email and surfing the internet. Most of my books are Kindle editions and the Kindle for Android app works fine for reading them on my HD+.
If you are only going to own one device, my recommendation would be the PW since you want a lighted e-ink reader and are already a Kindle owner. However, if you can afford it, I'd recommend that you consider a 9" or 10" tablet as a secondary device. I'm fairly certain you would prefer the larger screen for Safari Books Online and for the other uses I've mentioned above. If cost is an important consideration, you can't do better than the HD+ at $149 and frequently as low as $109 to $119 for certified refurbs if you search around for them.