Never got Star Trek nor Dr Who but I've nothing against you Trekkies. May the force be with you....Sorry wrong film, beam me up Bluemoon
Star Trek is about humanist ethics and philosophy with a strong anti-war message.
Doctor Who is about God and the morality of interventionism. They're opposites in that way - the Doctor serves as a deity who ultimately powerful whereas Trek is about a Universe where humans cannot rely on deities.
Q serves as God in Trek. He's untrustworthy, suspicious, nefarious and cruel. Humanity would be better off without him.
The Doctor serves as a God in his programme and he's moral, brave, strong and wise. Humanity would be lost without him.
Star Wars is a Japanese Wild West film set in space.