FWIW I hear this is a RAM/memory issue, and not limited to one specific phone. It could be that the Droid Turbo has more bloatware taking up more memory, but not sure.
I have a Galaxy S5, which is even older gen with less memory (2 GB vs. 3 GB). I crash constantly, doing pretty much anything that requires communication with the PoGo server.
The worst is when I get a text message/call while playing. The game freezes, gets to about 180 degrees, and usually force closes.
OR when I hatch an egg. MAN, the game hates when I hatch an egg. Any time it freezes I know to look at my recent Pokemon list for hatches.
I have the worst problems when looking at Pokemon List. Medals also, but not as bad. I have to restart halfway through evolving b/c by the end my phone is hot to the touch, evolves are taking 2x as long, and the screen starts being unresponsive/laggy. Any time I'm changing the names, it starts getting laggy too.
Gym battling I used to crash every 5-6 battles but that's gotten MUCH better.
Funny part is, I have almost no problems with regular gamplay outside of the menus/lists. Just walking around and catching Pokemon is fine.
What helped a lot was moving every possible app to the removable SD card. Then I uninstalled any app I didn't need, and disabled any possible app I could which I never used but Google forced on me (there are a lot)
Finally, I got the app 'greenify' and I manually hibernate anything I'm not using to avoid push notifications/background data while I"m playing.