Before we start, lets get a few acrynoms out of the way:
Flat Bottom Steering Wheel(FBSW) - no controls but flat bottom
Multi-Function Steering Wheel(MFSW) - Has stereo controls but no flatness
Flat Bottom Multi-Function Steering Wheel(FBMFSW) - has it all
Most Audi wheels are all physically swappable. However, there are two things to consider when swapping with another platform.
2-Your well being, ie airbag compatibility
or vise versa, which ever you value more.
1-There are pretty much two types of MFSWs. Some have a MODE button on the left, some dont. Only those with the MODE button will work with the B6 platform. Otherwise you'll end up with useless buttons, and no one wants that. edit: but I do!
2-All B6s* came with Single Stage Air Bags(SS or SSAB), but no flat bottoms. B7s and most newer Audi's came with Dual Stage Air Bags(DSAB) and this is when the flat bottom rage started. B7 RS4 has a nice flat bottom set up, but they are DSAB.
Herein lies the rub. My B6 single stage bag doesnt connect to the dualness of the newer wheels. There is a procedure to link the B6 single stage to the High Impact of the dual stage bag. However this has never been tested... Its a well debated topic online and most avoid it. Therefore B7 and most newer wheels are out of the question.
Audi TTs(8v or 8s) models(8v/8s is is the B6 to my S4) come with single stage air bags.
The 8vMkII style wheels have a gianormeous blimp of an airbag cover, and most came with the MODE button. You can even blank off the multifunction buttons if want. But the airbag size wasnt my style, so they were out of the picture.
The 8sMkIII style wheels have a lil button sized airbag in comparison, however coming across one with a MODE button is close to impossible... and no blanks available. But I managed to find one with a MODE button after a long search. I am took a chance with this as no one has tried this to see if it would work. In theory it would, but i'll jump to the chase, it didnt.
If your b6 is like mine and does not have any multifunction buttons from the factory, then you'll need a few new parts to make it all work:
Control Module - 8E0-953-549-R or Q
S/C Ring - 4E0-953-541-B