If we extract the plant secondary metabolites with organic solvents in cold solvent extraction and soxhelt extraction. The extracts that we get contains same compounds or soxhelt extraction gives more compounds.
There are two main differences between cold and Soxhlet extraction: the equilibrium and temperature. In one single stage extraction (may be in cold) the mass transfer of solutes is limited when the underflow (the mixture of solids with extract) reach equilibrium with extract. In Soxhlet due to the cyclic extract evacuation avoid the equilibrium. Soxhlet is for analytical purposes, 1 single stage extraction is for process purposes. In processes the extraction yield may be increased with multi-stage extraction, but the equilibrium always limit each stage. Moreover like Soxhlet is performed in solvent boiling point the solutes solubility may be different with respect to cold.
While soxhlet extraction is preferred to cold maceration by most phytochemists, it is not recommended when dealing with heat labile compounds. You can have same compounds using both methods but in that case soxhlet would give more yield. However, for heat labile phytoconstituents, go for cold maceration.
Soxhlet extraction is preferred as compared to cold extraction, because temperature difference and equilibrium difference. Furthermore, the polarity and dielectric constant at high temperature also make the difference