Is greater jihad the most important jihad or is the best jihad the one with the best intentions?

Hi the greater jihad is more important as this is the struggle Muslims facewithin themselves in order to make them closer to Allah and better muslims for example studying the Qur'an, attenfing their mosque, doing good deeds etc. Also the lesser jihad is about more a physical struggle/war showing that although their Qur'an teaches peace war is acceptable for them in circumstances as a last resort, if it's fought for a just cause, when the aim is to restore freedom etc. This info is from my revision guide hope it helps! :)