The Moto-X changed that. It feels smoother than my wife's iPhone 6+ (she has almost no apps installed other than those that came with the phone), gesture controls are actually very useful and well thought out and Motorola phones don't have as much crapware as other Android phones (still more than iPhone though). My wife still beats me with battery life (she charges her iPhone every 2-3 days if she thinks about it) but the Moto-X 2nd gen lasts a full busy day and I am perfectly happy with that (I must add that I am on 4G all day, I have unlimited data and do not connect to my employer's wifi neywork). My wife's iPhone 6+ skips briefly when you rotate a video from vertical to horizontal, my Moto-X does not (on the same program). That was a surprise.. The Moto-X definitely made me a qualified Android fan. Everything happens instantly, the phone has never crashed or needed rebooting in the month since I have had it. Finally, Motorola phones stay in your hand better than any other and don't hit the pavement as much because of the texture on the back. Talk to somebody who owns one.
You could do much worse than get a Moto-X 2nd gen.