There isn't a fixed difference between Sunnis and Shi'is for determining the beginning of the month of Ramadan. However, many Sunnis follow the announcement from Saudi Arabia for the beginning of the month of Ramadan. Unfortunately, sometimes, Saudia Arabia announces the sighting of the moon at a time when it is astronomically impossible to see it. (One can verify this using astronomical software) 

Most Shi'is follow local moonsighting (or via a shared horizon; either via the naked eye, as per Ayatollah Sistani, or with the help of an optical aid, such as Ayatollah Khamene'i). Some Sunnis do this also. 

Where one is in the world also affects differences in determining the beginning of the month. (You can visit moonsighting.com to see graphs of where the moon is visible and when.)

Anyway it is fine to fast on the last day or days of the month of Sha'ban, but counting the days of the month of Ramadan is useful for observing laylat al-qadr.