I believe that our physical world overlays the spiritual one. In the same way you put on a coat. In the highest realm we know in Jesus all things have their consistency, or are held together:
Col 1:17 And he is before all things, and by him all things consist.
Col 1:17 God's Son was before all else, and by him everything is held together.
So even demon powers, which are created have their consistency in Christ. That should be enough to know that demons are subject to Christ. We are joined to Christ by the Holy Spirit, so like the disciples, we share power over them.
As for which realm is most real, each is as real as the other, we live in the natural realm so should be more focused on the natural. But there are times when the spiritual forces of darkness want to influence our worlds for evil, it is at those times that we need to have faith that a) God has given us power over those things and tell them to leave, b) but if God allows natural suffering to occur (inspired by the evil one), and it does not change instantly, we must endure patiently (like Job), and we will receive the crown of life promised to those who endure.