Brendan Tighe, who was a Scientologist for 30 years, claims he witnessed this rivalry where the two actors were competing for the position under leader of the church, David Miscavige, reports dailymail.co.uk.
"Cruise is the only celeb with a direct line to Miscavige. Travolta and Kirstie Alley don't have that. Travolta doesn't get anything free, no one is giving him absurd gifts like an airplane hangar, custom-made bikes or over the top favours," said Tighe.
Cruise also received the Freedom Medal of Valor, the highest award in Scientology given to its most dedicated member, at a special gala in the UK in 2008.
While Cruise receives the special treatment, Travolta felt he was the "favourite son" of leader Miscavige before the "Jack Reacher" actor came along, according to Tighe.
"It's no secret that Cruise and Travolta despised each other. Travolta wasn't invited to Cruise's wedding with Katie Holmes, it told me everything. I can assure you Travolta doesn't recognise Cruise as a superior in any way. When Cruise got that medal Travolta was so p***ed off," he said.