The comparison here is the earthy tabernacle and the more perfect tabernacle...the types and fulfillments that are fashioned after the realities. God in our Lord Jesus Christ tabernacles among us and as He talks about the better and more perfect tabernacle is it without a doubt Christ!
The Tabernacle:
In the O.T. there was the priesthood and the picture of God dwelling with His people. The tabernacle that was separated from the others with the high priest able to go into the Holy of Holies once a year with blood. It was only a picture and was not manifested yet, but now we deal with Christ! That which was two in the O.T. now becomes one! He now dwells with His people with a more perfect tabernacle and Christ merges the priesthood and tabernacle being the perfect Priest and the perfect tabernacle. The O.T. blood sacrifices did not atone for sins and the people went to Glory on an "I owe you." But God prepared Him a body (sinless) to tabernacle (God with us) and by a new way makes a presence into the most Holy place with God! Through His flesh (the veil) He gives us entrance into the Living God!
Our Redemption:
By His own blood He enters the veil to the most Holy place on the cross and as He gave up the Ghost the O.T. temple veil is ripped from top to bottom and becomes an "open tabernacle" and God though Christ (who is the veil) allows us to stand now in the presence of the Living God in our Lord Jesus Christ who stands in God's presence with His blood and our covering of our sins. We can now have constant communion and fellowship with Him!
In the O.T. they only could see the picture. But we see Christ and have constant fellowship with Him and have a taste of that eternal fellowship with Him as we live, move, and have our being with Him. We taste of that at communion as He communes with US!