Perhaps we can answer this question by providing a deeper understanding of these twin holy days. We often find two expressions used to denote fear of Heaven: Yiras Shamayim, which means fear of Heaven, and Yiras Chait, meaning fear of sin. What is the difference between these two ideas? Also, Chazal tell us that in the recital of the daily Shema, the first paragraph is Kabalas ol malchus shamayim, the acceptance of the yoke of Heaven, and this takes precedence over the second paragraph, which is Kabalas ol Mitzvohs, accepting the yoke of Mitzvos. Again, what is the distinction between these two concepts?

Rav Simcha Zissel Ziv, commonly known as the Alter of Kelm, differentiates between the two expressions in the following manner. The first, fear of Heaven, signifies the intellectual comprehension of the punishment involved in sinning. It is this fear of future discipline that inhibits the person from doing the sin, much as the penalties of the law act as a deterrent to prevent people from breaking the law. Fear of sin, on the other hand, is a much more sophisticated level. This is the realisation of the great harm and damage caused by sin. Nobody sticks his hand into fire or runs across the freeway smack in the middle of rush hour traffic. This isn't fear of the heavy hand of the law; it's the basic instinct of self-preservation at work. So too, there is a superior level of worship whereby one feels an abhorrence of sin to such a degree that he perceives the raging fires of purgatory in the very sin.

Rav Mendel of Slutzk once commented regarding Rav Yoshe Ber Soloveichik, author of Sefer Bais Halevi, that the latter will not be granted reward for refraining from misdeed. His fear of sin is so developed, said Rav Mendel, that it is impossible for the Bais Halevi to sin. However, he will be rewarded for advancing his fear of sin to such an extent.

Similarly, Kabalas ol malchus shamayim is accepting upon oneself the sovereignty of the Almighty: The acknowledgment that there is an Omnipotent and Omniscient Hashem who keeps track of our deeds and there will yet be a day of reckoning and a price to pay for sinning. Kabalas ol mitzvohs is the higher step of yiras chait, the terror and mortal fear of the inherent danger of sin. This is why the one leads the other in the Shema, because this is the path of ascending stages of divine service. First, one must reach the position of serving Hashem with yiras shamayim, and subsequently, to strive for the ultimate degree of yiras chait.

We may safely say that Rosh Hashana and Yom Kippur reflect these two rungs. Rosh Hashana, the first day of Creation, commemorates the day that Hashem ruled over the universe. On this day, we proclaim Hashem's sovereignty over the entire world. By extension, this includes our undertaking to be His subjects and follow His commands, with commensurate reward and punishment to follow. Yom Kippur, the Day of Atonement, is the deeper level of fear, yiras chait. By integrating and absorbing a genuine fear of sin, we are deserving of having our previous sins erased. Thus, we can paraphrase the words of Chazal as follows: "Why does Rosh Hashana precede Yom Kippur? So that we should first accept upon ourselves the yoke of submission to Hashem's Rulership, and afterwards assume the yoke of mitzvah observance." May we merit success in achieving those lofty goals.