different things, and everybody will be a bit different. I'd go to a running store, where you can try a dozen or so different types of shoes. I know they tell me what kind of runner I am, but realistically, they can't tell a whole lot by watching you run on a treadmill or down a sidewalk for 20 seconds. It's mainly going to be feel.
To answer your question, I've run in only Brooks and Saucony for the last 8 years or so, but decided to give the Nike Air Zoom Pegasus 37s a try. Going from my Brooks, which were a bit more sturdy but heavier, and my Saucony's, which were lighter but less sturdy, to the Nike's, I hated them the first run I went on. They felt clunky and it took me a run or two to adjust the laces to get the same tightness. I was a borderline 2E width shoe and I decided to do standard width Nike's. It was an adjustment to change from lacing up my old running shoes as tight as I could to loosening up my Nike's and tightening them a lot more gingerly. Secondly, the Nike's were far more cushioned and I found my knees and legs were still running as if they were in the old shoes, making the run feel clunky. As I said, I hated the first run, but after adjusting the shoelaces and adjusting to the cushion, I like them way better than my old ones.
TLDR; It'll take you some time to find a shoe that fits you well, but you want one's that work well for you. Plan to try a handful before making a decision.