The main issue of difference between Shia Muslims and Sunni Muslims in Wudhu is the matter of wiping over the feet or washing them. Authentic evidence in Quran and Hadeeth is very clear that the Prophet (SAWA) was wiping over his feet in Wudhu. All Ahlul Bayt (AS) and pious companions (Sahabah) and Tabi'een did the same. These are some authentic Hadeeths in this regard:
1. In Musnad Ahmad Ibn Hanbal, Musnad al-Asharah, Musnad Uthman, Hadeeth number 456: Uthman ibn Affan performed Wudhu by taking water in his mouth then inside his nose, then washed his face and his two arms and wiped over his head and his feet. He said then: I saw the Messenger of Allah (SAWA) performing Wudhu like this. He asked number of companions who were present: O people, is it not? They replied him: Yes.
2. In Sunan ibn Maajah, Hadeeth 453 and in Saheeh al-Targheeb WAL-Tarheeb by Al-Albani, page 208: The confirmed authentic Hadeeth (Saheeh) from Rifaa'ah ibn Raafi' saying: I heard the Prophet (SAWA) saying: No Salah is perfect from any one until he performs Wudhu as Allah has ordered: Washing his face and hands from the elbow and wiping on his head and both feet.
3. In Mussannaf ibn Abi Shaibah (who was a teacher of Bukhari), Kitab al-Tahaaraat, Hadeeth 55: Uthman ibn Affan said: I saw the Messenger of Allah performing Wudhu by taking water in his mouth and nose then washing his face and his both hands and wiping over his head and upper part of his feet.
4. In al-Mu'jam al-Kabber by Tabarani, Hadeeth 3337: Abu Malik al-Ash'ari told his people: Come together so that I pray in front of you the Salah of the Mesenger of Allah (SAWA). They gathered and witnessed him performing Wudhu by washing his mouth and nose and washing his face and his both arms and wiping over his head and his feet, then he led them in Salah of al-Dhuhr.
5. In Saheeh al-Bukhari, Hadeeth 5352: The Prophet (SAWA) performed Wudhu by washing his mouth and nose and washing his face and hands and wiping over his head and feet.
6. In Sunan Ibn Maajah , part of Al-Taharah, Hadeeth 451: Ibn Abbas said: People (ignorant masses) are washing their feet in Wudhu, but I find nothing in Quran but wiping over the feet.
7. In Mussannaf Ibn Abi Shaibah, volume 1, page 30, narrating from Ali Ibn Abi Talib : I saw the Mesenger of Allah (SAWA) wiping over his feet (in Wudhu).
8. Mussannaf Abdul Razzaq, Hadeeth 53 on Wudhu, narrating from al-Shi'bi : Jabrael came down from Allah with the order of wiping over the feet.
9. In Tafseer al-Tabari , V. 6, P. 175: Ibn Abbas said: Wudhu is two washings ( face and arms) and two wiping (over head and feet). الوضوء غسلتان ومسحتان.
10. In Tafseer al-Tabari , Hadeeth 10433: Narrating from Abi Hamza al-Hajjaj (the well known tyrant) was ordering people wash their feet in Wudhu but Anas ( the companion) said: Allah is the truthful and Al-Hajjaj is a liar, and he recited the Verse: and wipe over your head and feet.
These are just few Hadeeths to prove that the Prophet (SAWA) was always wiping on his feet in Wudhu.
Many books were written in this subject by different authors who tried to justify their own sect but among the authentic ones is the well known book named Wudhu al-Nabi وضوء النبي by Sayyed Ali al-Shahristani.