This question appears again and again with an enviable regularity so I decided to cover it separately in article that was where to refer.
So that we know. AE version assumes older lens with other design of a diaphragm, than MM version and other bayonet joint. The Carl Zeiss firm reports that optical difference isn’t present, but on separate lenses enthusiasts managed to squeeze out recognition in optical improvement of a lens of MM version.

MM-lenses are precisely advanced

These lenses were improved optically upon transition to MM version by recognition of Carl Zeiss
— Distagon 2.8/25
— Distagon 2.8/28
— Sonnar 2.8/135

Provided below — are unconditionally improved

— Planar 1.7/50
Precisely it was optically improved around serial numbers 8xxx. One of users compared lenses 50/1.7 to serial numbers 5x, 6x, 7x and 8x and reported that improvements in the version 8x were impressive.
— Planar 2/135

It was completely remade by anniversary of the optical scheme Planar which was celebrated by Carl Zeiss firm for the reason that there were a new law concerning safety of production and some materials used earlier in optical glass. Respectively it compelled engineers of Carl Zeiss to count completely the original optical scheme of a lens for use with new type of glass.
Thus we know that Planar 2/135 of MM version differs from the previous AE-version but that we don’t know — it became better or worse.

Perhaps advanced MM lenses (on hearings)

In this case Carl Zeiss didn’t recognize improvement.
check of hearings: Orio,
— Distagon 1.4/35 (I tried both — the hearing didn’t come true)
— Distagon 2.8/35 (I tried both — the hearing didn’t come true)
— Planar 1.4/50 (I tried both — the hearing didn’t come true)
— Planar 1.4/85 (I tried both — the hearing didn’t come true) — article
— Planar 2/100 (I tried both — the HEARING CAME TRUE)
— Planar 2/135 (I tried both — the hearing didn’t come true)
— Sonnar 2.8/180 (I didn’t try new versions — it is impossible to confirm or disprove)

Frames of lenses

Some lenses upon transition to MM version replaced the frames. Among such lenses Sonnar 180 and Tele-Tessar 200.

Sonnar 85 changed the frame — by result of comparison of all 4 versions of lenses (AEG, AEJ, MMG and MMJ). Optically — the enlightenment was changed.
MMG version demands thicker adapter in order that didn’t cling a mirror on 5DmkII in comparison with the MMJ version. Both AE versions worked and with the ordinary, thin adapter, didn’t cling for a mirror.

carl zeiss