The swab nor the saliva test is more reliable than the other. It is about providing a sufficient DNA sample so the lab can process your sample. Both kits will deliver sufficient DNA if the user does the collection properly.
Swab collection kits should be ordered by individuals who have the inability to produce saliva and/or spit into a tube. Babies, young children, those with dry mouth are great candidates for the Swab kit.
Saliva collection kits should be ordered by individuals who have the ability to produce sufficient saliva and spit into a tube. Most people above the age of 4 years old can spit into a tube. IMPORTANT: Drool does not suffice as it does not contain enough DNA. Saliva from inside the mouth is needed.
Be sure to follow the instructions exactly as stated on the package or in these articles: