What is the best smart phone for reading e-books?

I am not aware of any smart phone optimal for reading e-books since the screen is so small. I highly suggest going to a tablet for reading e-books.

If you were open to a tablet, then the best one to get for reading books is definitely the Kindle Paper White. If you want a smartphone, my recommendation would be something with a big screen like the Samsung Galaxy S4 or S5 or even the Samsung Note 3. Also, check out these phones http://yotaphone.com/m/en/ They have two screens and one is e-ink which I believe is very easy on the eyes when reading a lot.

Get a tablet, and enjoy reading as much as you want. A 7.9 inch(mini, acer 830) is better for reading, but you might buy the N7 2013 if that's in your budget. Its awesome.

Check Huawei's Mate7.  The screen is huge and crisp, the battery is just huge :) And it has tons of nifty features too, like fingerprint sensor (no more PIN's and still secure ;-), and the ultra battery mode, that lengthens the originally 2-3 days worth of battery life to over a week. In this mode you can not read, but still beats the usage of an external battery pack.Using the Kindle Reading app on a smartphone gives you the option to use multiple (online) devices for reading the same material, as all of those can be synced.For epubs on Android, I recommend the Pocketbook Reader app.

I have an iPhone 5s and a Note 3, so those are the main sources of my experience. Personally, I think the Note3 kills the iPhone for reading. The bigger screen is a huge help and it seems to handle PDFs much faster and with less page-lag. As an added bonus, it's easier to take notes or highlight with the stylus. Now that the iPhone6 is out, I suppose the screen issue is a draw, but I'd still give it to the Note for the external card storage of various libraries of large file sized pdfs.