Notice the text says that our possession is a better and abiding possession. It does not say that the possession we have in Christ is better because it is abiding, although this would make great sense. A possession that lasts is much better than one which can be lost, stolen, or destroyed (assuming, of course, that it is a valuable possession and not a disease or something). A lasting possession would be better than one which can be lost.
Hebrews 10:34 says that our possession is a better possession and an abiding one. Not only does our possession in Christ endure, it also is better than the possession we have on earth. We have many good possessions on earth—home, family, friends, money, hospitals. The text says that what we have in Christ is qualitatively better than what we have in these things. A hospital is good, but it points to a great physician and healer who is better. Family is good, but it points to a Father and a Son who are better. And so it is with every good gift on the earth. Our good gifts are reminders of the Father above who dispenses every good gift. The gifts are good; the giver is better… and abiding.