What kinds of reference letters sound best to letter readers? Since I'm only starting my mathematical career, I've only ever requested letters from my advisers. So I was wondering what kinds of letters sound good to people reading reference letters? How does a neutral but good reference from a famous researcher compare against a strong letter from someone not-as-well-known? 

This is admittedly very situation dependent and subjective. But I thought I'd solicit opinions anyway, since they're always interesting to read.

Edit: I'd appreciate it if you could share your personal experience too. When you were on a faculty hiring committee, PhD/postdoc admissions committee or anything else, what sort of letters had the most effect on you?
For the targets you mention, the perception of the letter is highly biased by prior familiarity with the letter writer. It's very common to say things like "Well Prof. X doesn't like anyone, so if they call this person 'decent' they must be pretty awesome", or "Prof. Y loves everyone, so this letter is more useful for what it doesn't say than what it does", and so on.

Having said that, some of the things that help me when I read a letter (for postdocs or faculty hiring)

(Caveat: I'm at a US university and am most experienced in reading letters from US-based researchers, so cultural differences are important)


Who writes the letter
the nature of involvement they have with the applicant: "was a student in my class" is barely adequate, "was my summer intern" is not terrible, "worked with as a colleague" is excellent, "was my Ph.D student" is important, but can also get downweighted. 
The level of specificity in the letter: "We worked on problem X and Applicant came up with the key idea and did all the work" is good. "We were stumped on problem Y for ages and Applicant made the breakthrough" is even better. "We all worked on this problem and Applicant contributed ideas to it" is lukewarm. 
Points of reference: "You've probably heard of Prof. Awesome who works in this area, and Applicant is awesome-er", or "there are 5 people on the market this year in this area, and Applicant is at least 2nd best". 
Things not said, or said in code: "Applicant prefers to work alone" could sometimes mean "Applicant is an obnoxious lout" or "Applicant has no social skills", depending on the context. "Applicant works hard at their presentation skills" could mean "they give lousy talks". And so on. Here again, some prior familiarity with the letter writer helps.