An eccentric and an equant, both with the same eccentricity of the eccentric, will have different speeds at the apsides. The equant has a greater difference of speeds at the apsides than does the eccentric. Tycho considers the Earth-Sun orbit to be a simple eccentric, which Kepler disproves in Part III, demonstrating an equant in the theory of the sun.
To create the same speeds at the apsides, Tycho must use a larger eccentricity, since he uses an eccentric rather than an equant. Therefore, his Earth-Sun distances at the apsides have too great a difference.