The mono mixes from Please Please Me until The Beatles (White album) were the "official" mixes. The Beatles themselves spent an incredible amount of time on the mono mixes, then handed everything off to the engineers (George Martin himself from Revolver on) to do the stereo versions.
Martin never liked the stereo versions of Help! and Rubber Soul, so those were remixed in 1987 by him personally. The 1987 remixes of those two (remastered, obviously) will be the versions sold individually and in the stereo set - the original stereo mixes will be included on the mono discs (the same way the mono and stereo were both included on the Capitol Albums boxed sets).
The original 1987 CDs used the mono versions of Please Please Me, With the Beatles, A Hard Day's Night and Beatles for Sale - the new ones will be the first time they've been released in stereo since their original vinyl releases.
Yellow Submarine, Abbey Road, and Let it Be were not released in a separate mono mix - they were the only three albums that were always meant for stereo. However, the mono box set will include (in Mono Masters, the mono box's equivalent of Past Masters) the never-before-released-in-any-form mono mixes of the Yellow Submarine songs (first half of the album), which is pretty awesome.
So to make a long story short:
MIXED BY THE BEATLES FOR MONO SPECIFICALLY, STEREO VERSIONS AN AFTERTHOUGHT:
Please Please Me
With the Beatles
A Hard Day's Night
Beatles for Sale
Help!
Rubber Soul
Revolver
Sgt. Pepper's Lonely Hearts Club Band (Paul McCartney has publicly stated that if you haven't heard Sgt. Pepper in mono, you've never really heard it)
Magical Mystery Tour
The Beatles
MIXED BY THE BEATLES FOR STEREO SPECIFICALLY:
Yellow Submarine*
Abbey Road**
Let it Be**
* = not included in its entirety on mono box set
** = not included at all in mono box set
The mono mixes of Revolver, Sgt. Pepper, and the White album are quite different from the stereo versions - I prefer them myself (especially Pepper - the added vocal distortion on "Lucy in the Sky with Diamonds" improves the song tremendously), and I'm quite disappointed that the stereo versions are now the "official" versions, since they aren't the ones the Beatles put all their effort in.
Bottom line: At least listen to the mono Pepper - it's vastly superior to the stereo version. If you like it, try listening to the other mono versions.
The stereo box set also includes Past Masters, but many of those songs were never mixed in stereo, and the ones that have mono mixes are included in the Mono Masters disc - I wonder if they're using new stereo mixes, or if the mono mixes will just be duplicated on both box sets ...