Offshore oil is when companies drill for oil that is out in the ocean and they drill under the ocean floor. They then extract the oil and have it come up. Onshore drilling is when the oil is extracted by drilling on the land underneath the earth. Then extracting it and having it come up. Both types are now quite easy to do compared to the past.
It seems that the oil is the same since it is used primarily to make the same type of fuel. Both onshore and offshore drilling require big pieces of equipment and lots of money to be able to dig that far down to extract the oil. Therefore, both types of oil are used for the same purpose so there is no better oil.