Honestly, they're very similar. Lots of little things changed in small ways, but hardly any big things did.
The thing to remember is this: lots of people in the 80s didn't really play AD&D 1st edition as written, they ignored most of the war-gamer and medieval-history-buff cruft and took the bits that weren't overly complex. They were really just playing basic D&D, but with AD&D's races, classes, and alignments.
AD&D 2nd edition made all that extra detail optional, so that at core it pretty much was just basic D&D, but with AD&D's races, classes, and alignments.
Everything else is just fine print.