'Totally new or renewed creation?' is the question (see previous post). My money is on the eternal home of God's people being a renewed version of this creation.
Some have suggested that just as humanity has to die before resurrection can occur, so too there has to be a 'death' of creation before it is reborn. And (so the argument goes) just as a Christian's death (now through union with Christ in his death, physically in the death of the present body, then finally at judgment day) involves considerable destruction, we should expect a similar level of annihilation of the old in the production of the new heavens and earth. Man is so corrupted by the fall that a totally new man is needed - we should expect the same with the rest of creation.
There are several things that come to my mind in response to this.
1. When God made the world and declared it good, he meant it. But then of course the fall and the curse came. Humanity and the creation were both changed and marred by the events of Genesis 3 and following. This much is true.
2. However, there is (to my mind) a considerable asymmetry in the effects of the fall on humanity on the one hand and creation on the other. Humanity fell and became willfully ignorant of God and idolatrous, morally depraved, legally guilty and therefore deserving of death as a just and logical sentence. The creation was put under bondage to decay - a kind of 'death' perhaps corresponding to (and definitely related to) the death humanity faces. Yet Creation itself did not become sinful or evil in and of itself.
3. The good creation was subjected to frustration as a part of the judgment of humanity. Consequently it will be liberated when humanity is redeemed (Romans 8:19-21).
4. Even in the example of resurrected and restored humanity there is still considerable continuity between pre- and post-resurrection. It is still 'you' who will be raised (1 Corinthians 15 uses the analogy of a seed and its plant).
5. If all of this were not the case, then Satan would have succeeded in his war against God's good creation. God has to resort to annihilation and replacement for his plans for a created order (of some sort) to succeed. The good creation of Genesis 1-2 is resigned to the dustbin of eternity because of Satan's schemes. If the creation is renewed however, Satan ultimately fails.
No doubt there's more to be said. But, in conclusion, while there may be some sort of radical transformation of the present creation (depending on how you take 2 Peter 3:10 for example), there will be considerable and substantial continuity between it and the new creation.