And of course it depends on the engine type as well.
From the
Contrail Science web page there is a photo (from a German study on the subject) of two planes at the same altitude. The A340 leaves a contrail and the 707 does not - different engines.
And there is a perfect example for Jodie below that, of a rocket launch photo that shows only a partial contrail as the rocket travels through moist air, and none in dry air.
That page also has very good examples of why you just can't estimate altitude of aircraft accurately from the ground too.
A very handy website, as it covers most of the bunk being discussed here - with references, not just blind assertions.