The complete explanation of the Machlokes is dependent on the different ways the Machlokes is explained in the Gemara. However, on the simple level we may explain as follows:

Rebbi Eliezer holds that it is less of an Ones if the Korban a person was going to be Makriv had no way to be Karev b'Heter, and therefore he cannot be considered a To'eh b'Dvar Mitzvah.

Rebbi Yehoshua, on the other hand, holds that what makes the sin less of an Ones is when a person is trying to do something Asur (such as bringing a Pesach l'Shem Shelamim, since a Shelamim may not be brought on Shabbos), as opposed to when a person is trying to bring a Shelamim l'Shem Pesach, since his intention (offering a Pesach) is Mutar on Shabbos.

D. Zupnik