Christ has obtained a ministry that is as much more excellent than the old as the covenant he mediates is better, since it is enacted on better promises. The New Covenant is not an improved version of the Old. It is fundamentally different.
In the Old Covenant, a curtain stood between God and man. In the New, the curtain is torn. Christ is the mediator, and through him you have direct access. No priestly hierarchy, no temple system, you and the Father, face to face.
If God feels far away, it is not because he has withdrawn. The nearness stands. The access is open. The Spirit in you testifies: You belong.