An anonymous commenter eloquently summarized the heresy of Sasson and Simchah as follows:
The heresy of Sasson, then, would be that the ikar is attaining faith, understanding, and morality. They can be achieved without (all) the Mitzvot, and once they have been achieved, the Mitzvot have no purpose. And this reflects what is seen in the religion of Edom: Only faith.
And the heresy of Simcha would be that there is only the performance of Mitzvot. Halacha provides and defines everything. There is no morality outside of it, and no Hasagot of any kind. Simcha does not care much about the faith of the orthodox Jew. He does not care much about the Jew's spiritual level. As long as he learns Halacha and lives it. Simcha discourages learning "other things", like Sod, or Science. Our whole purpose is to serve HaShem by doing the Mitzvot. And this reflects what is seen in the religion of Yishmael.