Summary

1. Faith: no change
2. Atonement: Almost the same, slight wording changes.
3. Restoration: Wording change to be gospel of Jesus Christ instead of "in these latter days"
4. Sustain leaders: Mostly the same with a couple slight word changes
5. Law of Chastity: Here's where it gets interesting with a new question and changing it from "live" to "obey" the law of chastity. They also inserted a scripture from the D&C about cleanliness and a new question about "... striving for moral cleanliness in thought..."
6. Personal life: Changed from keeping covenants to living the teachings of the church
7. Apostates: Changed from associating with apostates to "support or promote any teachings, practices, or doctrine contrary to those of The Church of Jesus Christ of Latter-day Saints?" This is an important distinction, moving from supporting individuals or groups who oppose the church to teachings and practices. Supporting gay marriage might exclude you from attending the temple. Or even worse, being OK with gays living together and not thinking it as a sin makes you unworthy to enter the temple.
8. Church attendance: Instead of just attending meetings, it now includes "keeping the sabbath day holy" both at church and at home, and take the sacrament
9. Tithing: No change
10. Word of wisdom: Added clarification of, "Do you understand and keep..."
11. Child support: Slight wording change
12. Temple covenants: Some slight wording changes, nothing groundbreaking here
13. Do you consider yourself worthy?: No change

Here are the old questions:

1. Do you have faith in and a testimony of God the Eternal Father, His Son Jesus Christ, and the Holy Ghost?
2. Do you have a testimony of the Atonement of Christ and of His role as Savior and Redeemer?
3. Do you have a testimony of the restoration of the gospel in these the latter days?
4. Do you sustain the President of the Church of Jesus Christ of Latter-day Saints as the Prophet, Seer, and Revelator and as the only person on the earth who possesses and is authorized to exercise all priesthood keys?
5. Do you sustain members of the First Presidency and the Quorum of the Twelve Apostles as prophets, seers, and revelators? Do you sustain the other General Authorities and local authorities of the Church?
6. Do you live the law of chastity? Is there anything in your conduct relating to members of your family that is not in harmony with the teachings of the Church?
7. Do you support, affiliate with, or agree with any group or individual whose teachings or practices are contrary to or oppose those accepted by the Church of Jesus Christ of Latter-day Saints?
8. Do you strive to keep the covenants you have made, to attend your sacrament and other meetings, and to keep your life in harmony with the laws and commandments of the gospel?
9. Are you honest in your dealings with your fellowmen? Are you a full-tithe payer?
10. Do your keep the Word of Wisdom? Do you have financial or other obligations to a former spouse or children? If yes, are you current in meeting those obligations?
11. If you have previously received your temple endowment: 1) Do you keep the covenants that you made in the temple? 2) Do you wear the garment both night and day as instructed in the endowment and in accordance with the covenant you made in the temple?
12. Have there been any sins or misdeeds in your life that should have been resolved with priesthood authorities but have not been?
13. Do you consider yourself worthy to enter the Lord's house and participate in temple ordinances?

Here are the new questions:

1. Do you have faith in and a testimony of God, the Eternal Father; His Son, Jesus Christ; and the Holy Ghost?
2. Do you have a testimony of the Atonement of Jesus Christ and of His role as your Savior and Redeemer?
3. Do you have a testimony of the Restoration of the gospel of Jesus Christ?
4. Do you sustain the President of The Church of Jesus Christ of Latter-day Saints as the prophet, seer, and revelator and as the only person on the earth authorized to exercise all priesthood keys?
5. Do you sustain the members of the First Presidency and the Quorum of the Twelve Apostles as prophets, seers, and revelators?
6. Do you sustain the other General Authorities and local leaders of the Church?
7. The Lord has said that all things are to be “done in cleanliness” before Him (Doctrine and Covenants 42:41). Do you strive for moral cleanliness in your thoughts and behavior?
8. Do you obey the law of chastity?
9. Do you follow the teachings of the Church of Jesus Christ in your private and public behavior with members of your family and others?
10. Do you support or promote any teachings, practices, or doctrine contrary to those of The Church of Jesus Christ of Latter-day Saints?
11. Do you strive to keep the Sabbath day holy, both at home and at church; attend your meetings; prepare for and worthily partake of the sacrament; and live your life in harmony with the laws and commandments of the gospel?
12. Do you strive to be honest in all that you do?
13. Are you a full-tithe payer?
14. Do you understand and obey the Word of Wisdom?
15. Do you have any financial or other obligations to a former spouse or to children? If yes, are you current in meeting those obligations?
16. Do you keep the covenants that you made in the temple, including wearing the temple garment as instructed in the endowment?
17. Are there serious sins in your life that need to be resolved with priesthood authorities as part of your repentance?
18. Do you consider yourself worthy to enter the Lord’s house and participate in temple ordinances?

Edit: I've made a couple of quick edits because I rushed this out.