Summary: YYYY-MMM-DD is better because you don't have possible confusion.
Steve Krug, a usability consultant and author says "Don't Make Me Think" - i.e., you want to reduce the amount of thinking that users have to do (the cognitive load).
So using 1991-Nov-01 (or November) instead of 1991-11-01 is clearly a better approach because you don't, like @Alvaro says, have the confusion of 1991-07-01 being possibly 1st July or 7th January, thus causing users to have to sit and think about it.
@no comprende cites using Roman numerals for the month as per International Postal formats, but that hasn't cottoned on, thankfully. Why thankfully? Because that too requires that people sit and think about what the numeral is and then translate that to a month in their mind - better to just tell them what the month is straight away. Usually, a website is in one language, so, it doesn't need to be international, and if it does, you'd translate the month - e.g. "July" - into their language, so that it's never ambiguous.