I do both, actually. Vacations are so expensive and I don't get to take one often, so $15-$20 extra to duplicate the book is well worth it. I use the hard copy before I leave, it's a personal preference - I like the layout in hardback better. When I leave for the trip, I rip out the maps. If I'm in a foreign city for a while, I also order "Streetwise" brand maps, they save tons of time being lost in the city (although I realize sometimes lost is not a bad thing, but if you have reservations somewhere for a show, for example, it's not the time to be lost). While on the trip, I either take the Kindle or use my Samsung Note 4, which has approx. the same size large screen as the iPhone 6s Plus.
My personal experience is that if you use the Kindle app on your phone and use the large font, it's actually easier to look things up on the phone than the Kindle when you're walking along or standing in a line - less bulky, you're more accustomed to using your phone on the fly and it's one less thing to carry, because I'm not leaving my phone in the hotel room. I would think the size of your phone screen would greatly impact how well this works. In any case, the free Kindle app allows you to pay once for the book on Amazon and download it to multiple devices, phone, iPad, etc. Very convenient. The free PC or Mac version of the app makes for nice printouts as well. Don't forget to download your Rick Steve audio tours, there are also inexpensive walking tours on Audible.com of cities Rick doesn't provide audios for. Also, be sure to label your Kindle with contact information and password protect it, in case you leave it in the plane or somewhere else (I speak from experience). Enjoy your trip!