A Better Covenant?

Hebrews 8:6-13 (King James Version)
6But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises.
7For if that first covenant had been faultless, then should no place have been sought for the second.
8For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
9Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord.
10For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
11And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
12For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.
13In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away.

Hebrews 10:15-17 (King James Version)
15Whereof the Holy Ghost also is a witness to us: for after that he had said before,
16This is the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them;
17And their sins and iniquities will I remember no more.
Hebrews 10:15-17 (King James Version)

A better covenant which was established on better promisses?

Some suggest that a Christian can fail and lapse into a state of unbelief, and suffer for that at the Judgement Seat of Christ. If that is so then how is the New Covenant a better covenant? After all, according to them, the results are all the same - that is that those within the covenant can fall into unbelief just as the larger part of OT Israel had. These people then are teaching that the New Covenant is not a better covenant after all.