1) LISREL attempts to account for observed covariances, whereas PLS aims at explaining variances.
2) LISREL offers statistical precision in the context of stringent assumptions; PLS trade parameter efficiency for prediction accuracy, simplicity, and fewer assumptions.
3) Both models treat measurement residuals, but in different ways. PLS separates out “irrelevant” variance from the structural portion of the model; LISREL combines specific variance and measurement error into a single estimate and adjusts for attenuation.
4) LISREL requires relatively large samples for accurate estimation and relatively few variables and constructs for convergence; PLS is applicable to small samples in estimation as well as testing and appears to converge quickly even for large models with many variables and constructs. (Fornel and Bookstein，1982， p.450)