Can I transfer my Injustice game data from my iPhone to my new Android phone? I currently use an iPhone 4, and I'm eligible for an upgrade. I'm considering the Note 3 and the Galaxy S5.  I've been playing Injustice for some time now and I'd very much like to not have to go through all the trouble of re-earning all of the characters I've bought or won in challenges. Will logging in with my WBID on my future phone automatically let me transfer over my game data? If not, is there something else I could do?

Also, if you have any other suggestions for what I should upgrade to please feel free to suggest it.
Man, you're out of luck. Versions of Injustice for Android and iOS differ greatly. the iOS version generally gets updated months before Android. This affects what characters you can buy, what challenges you can complete etc. 

I thinks it's safe to say they're incompatible. And from my experience the Android version performs rather poorly compared to iOS. 

Considering all of the above I would recommend sticking to your iPhone for playing Injustice.