Whilst doing my PPL skills test I put on the transponder in mode C + ALTitude, as I would rather be 'seen' by any TCAS equipped aircraft in the vicinity and feel that information such as altitude, if available, should be given. Although I was not in controlled airspace I was underneath it.
At the test debrief the CFI said it was preferable not to give altitude information when flying below or near controlled airspace (unless specifically requested by ATC) as anything heavy passing overhead has the 'inconvenience' of changing autopilot mode to a vertical speed mode when they pick up your altitude data in the traffic advisory. If you are close enough you could also of course generate an RA which would be even more inconvenient for the Jet-A1 guzzlers !
Its no coincidence that the CFI is a jet jockey himself!