I was tempted. This spring, I figured I'd be deciding between the Note 3 and the iPhone 5S, and was actually leaning toward going with the Note 3.
Then, the last few months, the battery on my Galaxy S3 has been terrible. Sprint said that there wasn't anything wrong with the battery and that it was in good health. No amount of reformatting or adjusting settings would fix it. If I didn't kill any apps after I was done using them, they just sucked the battery dry. Being my first Android, I don't know if this was something I was doing wrong or what, but I didn't want to chance that happening again.
So far, the battery on my 5S has been great. MUCH better than my GS3, I assume because of the way iOS handles background apps vs. the way Android does.
I loved a lot about Android (especially the vanilla-ish Android I installed), but definitely not power management.