They are relatively the same, and mean the same, BUT "based on" is the more correct use of the preposition in the English language, leaving "based off" as a regional vernacular, meaning that although it is not correct, many people say it and every English speaker would understand you perfectly if you chose to say it also. It is similar the the use of ain't. Although it isn't correct to use, many people do, and all speakers would understand you if you made the mistake.