In this work the relationships between system composition, polymer–organoclay interaction, morphology and rheological response, under shear, and elongational flow, of different melt compounded polylactic acid (PLA)/organoclay nanocomposites are investigated, with the aim to properly select the better organoclay for a well-specified PLA grade and processing technology. Polylactide nanocomposites are prepared using two commercial polylactide grades (PLA 4032D and PLA 2003D) and two different organomodified montmorillonites (Cloisite 30B and Nanofil SE3010). FTIR analysis evidences the occurrence of stronger polymer/organoclay interactions for the system PLA4032D+C30B, resulting in a higher clay dispersion and exfoliation levels. Moreover, rheological tests at low shear rates show that, if PLA 2003D is used as polymer matrix (differing from PLA4032D by the presence of a high molecular weight tail), a better dispersed nanomorphology can be obtained with Nanofil SE3010, characterized by a double d-spacing compared to Cloisite 30B, despite the higher polar character of this latter nanofiller. On the other hand, elongational rheological measurements evidence for NSE3010-based hybrids a marked extensional thickening, whilst the stronger polar interactions between the phases in both the polylactide grades filled with C30B, determine increments in elongational viscosity, but inhibit the strain hardening behavior.