Generally, omnis can be more forgiving of on stage placement and setup configuration than directionals- partly because the primary factor in their setup is spacing alone and the angle between them is far less important to image (but may still be important to tone). In addition to being less tricky to setup to achieve a good, generally balanced if not razor-sharp stereo image, on stage is one of the places where omnis have a better chance of sounding good due to the direct/reverberant pickup of the pattern and proximity to the sound sources, where farther away in less than ideal situations, that aspect can be the biggest challenge in using them sucessfully.
Directionals can sound great on stage too of course, and sometimes may be the better choice, but they do require a bit more thought into which setup is appropriate. I guess my point is that I'd recommend using omnis as a simple starting approach for recording on stage because it works well most of the time- the 'path of least resistance'. I'd suggest setups using directional mics to those wanting to improve on something they otherwise aren't getting from the omnis on stage and are willing (like in this discussion) to put some thought into what angle and spacing combination is most appropriate for the situation. That assumes both omnis and directionals of similar quality are available, if not that should influence the decision as well.