I sense this topic might get out of hand rather quickly. Some people are intensely passionate about their brands!
For me however, I have always had Android smart phones (before that it was Symbian...). I have always dealt with Apple products at my work, and although they have their merits, I detest iTunes as a program (various reason). Which put me off the first iphone.
I used to like HTC phones for their software (Sense) and screens. Samsungs tended to anyways have nice cameras but I found their screen too vivid for my liking. As the Nexus line grew up I liked it more and more. So when the Nexus 4 was announced I bought it and I have never looked back. From now on I reckon I will always have a "pure" android phone rather than one with an OS overlay. I find overlays and bloat ware to be very annoying. And yes there are ways to get rid of them, but having to manually do that, then manually update the phone every to often gets boring after a while. Stock Android just updates, and is on the whole, fine with doing it. I also like getting new features first
Currently I have the Google Pixel.
Yes it costs a fortune for a phone. But for me it is worth it. The camera preforms very well in most situations, which is important to me. I do like being able to take quick pictures no matter where I am. I do find the pictures are rather "soft" when the light is low however.
A big part of me buying the phone was the inclusion of lifetime, full resolution photo and video backups with google. I have used Google Photos to automatically back up my phone pictures for years - February 2010 to be more exact! It works perfectly for me so having this without worrying about the ever increasing files sizes eating up my ever limited space on Google Drive was a massive plus for me. I may not have bought the phone if this was not included.
I've also had some fun using the 4K video and amazing slow motion on it. Seeing exactly how my pet parrot takes off and lands in slow motion is amazing
For me, a massive part of buying a phone is always about how it feels in my hand. I have quite small hands, so large screen phones can feel cumbersome to me. Especially if they have more weight at the top as this makes me feel like I am always close to dropping it when holding it.
I prefer the edges to be curved, but not the screen. I tried the curved screen on the Samsung, and found I was constantly pressing things I did not mean to!
The hard lines on the Sony's and the iphone I find too "clinical" and they are not a nice experience for me when holding them.
Materials used is also an interesting bit for me. I like smoothness. The smooth feel of glass, then a subtle change to metal or plastic around the edges is what I like. No "lip" around the screen is required. Same with the rear, no matter what it is made of, plastic or metal or glass. It should be smooth. If plastic, that slightly rubberized texture that is smooth, but grippy at the same time is great.
Part of this love for how a device feels means I never put my phones in cases. At most (normally when the back is covered in scratches) I will buy a vinyl "skin" from Dbrand in some striking colour (orange or purple are my favorites) and stick that on the back. It covers up the scratches, makes my phone look individual and with a bright rear, it is much easier to find with it slips down the side of a couch or such! The DBrand skins also come in various textures, which I like too.