Chattier authors are nice for providing context and intuition and sometimes details about the historical context, but I personally find them to be very distracting and a bit overwhelming. I don't like using them for much other than a reference or more casual reading. On the other hand, I loved reading a few sentences from Rudin that I didn't quite follow, then pulling out some pen & paper and doing a quick validation, or even going on a drive and munching on them until I understood
That's me though. I'm glad that there seems to be no shortage of introductory analysis texts written in all kinds of styles so that folks can find the ones that work best for them.
As an aside, I think it's a bummer that analysis classes often feel like hazing courses in the math curriculum, leading many mathematicians to despise it. I've been very lucky to have great analysis teachers, or at least ones that care very much about pedagogy over ruthless elitism, and conveying the beauty and fun that lies amid the ugly bit :)
Also, re Rudin: his autobiography is certainly worth reading, if for no other reason than for his account of surviving the Anschluss (the Nazi annexation of Austria during WWII) as a young Jew. One of my favorite bits:
"On the first day of school after the Anschluss several of our teachers and even some students strutted around in their shit-colored storm trooper uniforms. (The Nazi party had been illegal, but had obviously existed.) One of those was the gym teacher whom I had always disliked. He even had a pistol strapped to his belt. A few days later I heard that he had shot himself in the foot. This was one of the very few bits of cheerful news at the time."
It's a fairly harrowing read, and perhaps some of his best writing overall