Following the foundation laid out in the Basic set, the Expert set provided details for characters to advance in level to the approximately the mid-teen levels; I know it's somewhere around 14th or 15th level but it has been a while and my memory is a little fuzzy. The Expert set also focused more on wilderness and overland adventuring and encounters in contrast to the focus on the dungeon environment found in the Basic set. Of course, since the characters gained new options then were also new monsters, treasures, and other assorted information in these rules.
I have heard that there were actually adds from the old TSR catalog that had information for an unproduced Holmes Expert set. I have no idea if this is true or not. Regardless, all of us in the gaming group had a copy of the Mentzer version of the Expert rules. I do recall playing through the included adventure, Isle of Dread, and thinking how cool it was to go on a pirate adventure to an uncharted island.
For some reason, no one in the playing group owned a copy of the Moldvay version of the Expert rules. I think this is a case of somewhat odd luck because several of us had the matching Basic rules. I am sure the differences between the two Expert sets were not all that great but I would have preferred a copy of the Moldvay set. Judging from the cover, thet presentation matched the Basic set and the two boxes would have made a nice pair on the shelf together. I have also heard that there was a Moldvay Companion rules set that was unproduced also.
Out of all the D&D products that I have owned over the years, the product(s) I feel would be ideal for playing today would be the Moldvay Basic along with the matching Expert rules that I never owned. Most of our D&D campaigns rarely made it further than the levels presented in the Expert rules so these two boxed sets of rules would make an ideal rules set for my old gaming group. It's pretty tempting to head over to some used game sites to see if I can pick both of these up.