My experience from browsing around different online websites and social media platforms are that like most all other things, you will have fanboys and people who love the brand that they own and talk down upon the other.
I, like you, have heard both Dewalt and Milwaukee are great performers. Milwaukee seems to be the more often purchased. I currently have an older Dewalt 18v kit, as well as a 12v bit driver. I love them. However, I would eventually like to get a 1/4" and 3/8" cordless ratchet, as well as a 3/8" and 1/4" cordless impact, and they will both be from Milwaukee. My decision is made solely on the fact that more people have reviewed or commented positively on their performance than on the Dewalts. I have had zero problem with my Dwalts, up until a few months ago when the chuck started slipping on my drill. I can't fault it or be mad at it, because it's had a pretty tough 8ish years of life.
It seems like both brands do similar jobs. I'd imagine that the real-world feel of comparable tools between brands would probably be minor differences, assuming both tools were in good working order.
I would definitely buy Dewalt again, but when it comes to the tools that I want to get eventually that I listed above, I'll go the Milwaukee Fuel route.
I'm sure I'm going to get killed for this comment. I do have other Milwaukee tools, but none that are the equivalent of my Dewalt tools. I like them both, they're both respectable brands in my opinion.