The 1846-O Half Dollar is found with a Medium Date (Breen calls it a Small Date) and a Tall Date. Telling the two apart is actually quite easy: on the Medium Date, the bottom of the crosslet on the 4 nearly touches the right edge of the bottom serif of the 4; on the Tall Date they are widely separated. The Tall Date logotype was also used on some 1846 Large Cents.
The Tall Date 1846-O Half Dollar appears to be roughly twice as rare as the Medium Date version, based on the PCGS Population Report as of June 2011. Fewer than 40 examples have been certified by PCGS in all grades and only two Mint State examples have been certified by PCGS (both in MS-62).