Hi Scoobster,
the reason, why some jets leave those white trails, while others not, is altitude. The hot and humid exhaust from jet engines mixes with the atmosphere, which at high altitude is of much lower vapor pressure and temperature than the exhausted gas. The water vapor contained in the jet exhaust condenses and may freeze, and this mixing process forms a cloud very similar to the one your hot breath makes on a cold day.
Depending on a plane's altitude, and the temperature and humidity of the atmosphere, contrails may vary in their thickness, extent and duration.