There are various dates of birth of Prophet Mohammed, the point to be noted in these cases are most of the dates are narrated by Sahaba (Companions) of Prophet Mohammed.
Prophet Mohammed began to have companions after the age of 40 years when he declared himself as Prophet of God. Before the declaration he was considered just a virtuous man had few friends and no one was interested in when was he born. Amazingly, these people who later got converted to Islam, became companions started to narrate Prophet Mohammed’s biography, when was he born etc etc.
How did they knew when was he born? Most of Sahaba (Companions) had never witnessed Prophet Mohammed’s childhood as they were quite young or of same age. Those who were older to Prophet Mohammed most among them had died during the very life time of Prophet Mohammed. These same age people who became companions narrating biography of Prophet Mohammed about his childhood needs scrutiny.
These Sahaba (Companions) narrated their individual versions to the so called biographers who compiled books of Ahaadith (Anthologies), Seerah (Biographies) of Prophet Mohammed. Most of these people never questioned Sahaba (Companions) as to how come they know when was Prophet born on which date on what day? They just went on to record whatever was narrated to them.
A Sahabi (a Companion) who became Muslim in Madina narrated the birth, childhood and Makkan life of Prophet Mohammed in details and no one questioned him about how he gathered knowledge when he was not present. Just to make their books thicker and heavier biographers wrote whatever they heard from these Sahaba (Companions).
Sunnis began celebrating Prophet Mohammed’s birthday on 12th Rabiul Awwal during the caliphate of Harun Rashid; no record is available to show that Sunnis ever celebrated his birth before the reign of Harun Rashid. Their version of birthday is based on narrations of Prophet Mohammed’s companions of later life who never witnessed birth and childhood of Prophet Mohammed. Their version state the date to be 12th Rabiul Awwal (Monday) year of Elephant as most probable date, they also have other dates in their records from other companions which are 9th, 11th etc.
Shia all around the world celebrate the Birthday of Prophet Mohammed on 17th Rabiul Awwal on authority of narration (Hadith) narrated by Abu Talib the uncle and legal guardian of Prophet Mohammed from childhood unto his very death, Abu Talib died some time prior to Migration (Hijra) to Madina. It was rather Abu Talib’s death which triggered Migration (Hijra). Thus this narration whose chain of narration goes back to Abu Talib is considered most authentic among Shia.
Abu Talib narrated that his nephew Mohammed was born on 17th Rabiul Awwal in the year of Elephant, 53 BH (Friday). No one can question Abu Talib how he knew all these, since he was a close family member and had been legal guardian of Prophet Mohammed. Also, Shia had always celebrated Birthday of Prophet Mohammed even before the reign of Harun Rashid.
However, among 12 Imams (as) and other Ahlul Baet (Family of Prophet Mohammed) there are more than one version of births of some Imams (as) as well as that of other members, of which some dates are considered more authentic while others are considered less authentic. Thus, there is nothing wrong if one celebrates birth of Prophet Mohammed on 12th as well. Rather from 12th to 17th whole week is celebrated as Prophet Mohammed’s birth week.
Sunnis also consider the same date 12th Rabiul Awwal as the day Prophet Mohammed passed away, if you read Sunni records of the last day of Prophet Mohammed he became well and came out of house and offered prayers in mosque, later all of sudden became seriously ill and passed away by noon. If it was 12th Rabiul Awwal his birthday and Prophet Mohammed recovered from illness, why no one wished him in that regards?
Modern Salafi (Wahhabbi) cite the same reason when they declare that celebrating Prophet Mohammed’s birthday is forbidden and a sin in Islam. Actually, why no one wished him was because the day was simply not his birthday. Rather was not even month of Rabiul Awwal. Same dates of birth and passing away give rise to high doubt that dates were randomly chosen to fill up doubtful biographies.
Also to forbid the celebration of birthday by making it the death day as well, which was an Ommayyad tactic? This is why no record of Sunnis celebrating his birthday is found before the reign of Harun Rashid. Ommayyad period saw no such celebration, it was only Abbasid era of Harun Rashid which started celebration among Sunnis.
Shia consider 28th Safar 11 AH as the day Prophet Mohammed passed away. Shia had always celebrated his birthday as well as mourned the day he passed away, there are ample of records. Thus, it shows Shia history was not compiled in later periods out of some political need.Oh Allah! Peace and Salutation be upon Mohammed and House-hold of Mohammed.