I've got a note 4, and it's great does anything and everything, good battery life, 4k screen and camera and what not. But nower' days it's not necessarily specs and speeds with these flagship brand phones (SAMSUNG, HTC, ETC). Because whether it be iPhone with iOS or Samsung with android, with the iPhone having 1GB of ram and the Samsung having 3, they both run smoothly and what not as the softwares are different and they require different things.
As you said you don't want an iPhone, so within Android (as Windows are utter shite) if you're looking for speed, you want a flagship modal of a brand name such a Samsung, HTC, Sony, LG, Google. Whereas if your looking at just a phone that works with a decent battery you want to go with one of then Chinese ones such as Cubot and THL or the once begging with H -(
https://www.chinavasion.com/china/wholesale/Android_Phones/Large_Screen_Android_Phones/).
But like I said nower' days it's more camera and screen quality over speeds with the flagship models.
Either way my recommendation is a Samsung either a Note 4 (Or wait for the note 5) or S6, as their the flagships and are the creme of the crop.
P.S I'm really tired atm so sorry if it doesn't make sense haha
