Why do you see contrails from some planes and not others?

Because they're flying at different altitudes.

The condensation trail formations can be predicted by FAA weather shops based on expected humidity levels in different levels of the atmosphere - so a plane that's flying at say Flight Level 330 (roughly 33,000 ft, but not exactly-that's another question) may not be creating contrails; but one flying at FL380 is. Primarily due to the different levels of moisture in the air.