Talking about differences in spin recovery techniques, another plus point about including spin training in the PPL is that the effects of controls in a spin can be looked at. If you read a POH that maybe just says use pro-spin aileron to effect recovery I think it would be good for the pilot to understand why, and I'm not sure that is currently the case.
I also think when it comes to stalling, instructors should make a point of demonstrating how little forward stick/ yoke is required to actually unstall an aircraft. The full-power and shove the stick/yoke forward is over-dramatising what would otherwise be a fairly gentle and underwhelming recovery. Then using power to minimise height loss.
Inverted flight and effects of controls would be another good thing to include in the PPL, but since most trainers can't do it I guess it never will be included.