I guess it would depend on what playing skills you are planning to promote or show off...if doing a replication of a sax over a big band arrangement is your goal, then having a "full" accompaniment might be what you want.

If you want people to take notice of your piano skills, perhaps less accompaniment might give you more room to play, but depending on the tune and the genre, that may not always be the case.

They are called "arrangers" for a reason...every human arranger would put together a tune in a different way, each one believing it is right for him...some arrangers prefer dense backgrounds, and others may wish to have a minimal amount of orchestration...the arranger(the instrument) gives us that choice.

To me, all arranger play is some sort of fakery, albeit in a good positive light, not in a negative connotation.

In 99% of the cases, the audience do not care, as long as the performance has merit and/or entertains them.

Ian