Two axis vs one axis stabilization. Mode 2 just stabilizes lateral movements allowing for horizontal movements (i.e pans). If you pan slowly in mode 1 the IS will fight you.
My understanding is Mode 2 will stabilise correctly only in a horizontal (panning) situation whereas Mode 1 will counter correct movement in both up/down and side to side directions
The manual for my 70-200/2.8L IS says, "To pan a moving subject, select MODE 2. Mode 2 corrects vibrations and shaking only in the direction at right angles to the camera panning movement." IOW, it stabilizes for panning side-to-side and also for panning up-and-down.
Update. Here's what the manual says for the new 70-200/2.8L IS Mk II that I received today. "MODE 2: It compensates for vertical camera shake during following shots in a horizontal direction, and compensates for horizontal camera shake during following shots in a vertical direction."
Mode 2 works for vertical and horizontal panning. Vertical panning may be panning in the vertical direction or panning in the horizontal direction with the camera turned on its side (portrait mode). Mode 2 detects which direction has consistent or significant movement and which one has variable movement and switches off IS in the direction of the consistent or significant movement. Depending how fast or smoothly you pan it may get it wrong.
The other trouble with mode 2 is that if you pan diagonally - common when tracking birds or aircraft in flight - then mode 2 doesn't know whether to switch off the vertical correction, the horizontal correction, both or neither and your results can be messy or good depending on what it decides and when it decides.
Mode 1 is more consistent when panning diagonally in that it always tries to do both vertical and horizontal correction. The trouble is that it eventually runs out of correction room and has to reset, and if you take a photo during that process then it will look very blurry.
I use mode 2 for horizontal or vertical panning and mode 1 for everything else but I also tend to take bursts of multiple shots to help overcome temporary IS-induced blur. Another option is to disable IS altogether if I have enough shutter speed to work with.
