Before anyone accuses me of posting an Apple advertisement, I'll say that I am sure that recent phones from other brands have probably also improved a lot in terms of daylight usability. They all buy their screens from the same small group of manufacturers, after all. But what I really mean to point out is: if you have an older smartphone that is difficult to use in broad daylight, shop around and try some of the newer models.
I doubt you'll have much luck finding phones with e-ink screens. My experience running a modified version of Android on a Nook convinced me that that just doesn't work well; e-ink updates really slowly, and needs to be "shaken up" periodically (where the screen goes all black and then all white, before repainting the UI), all of which looks like crap when you're trying to use standard smartphone apps that are constantly doing things that e-ink sucks at, like scrolling or animations.