The semantic variant of a primary progressive aphasia (svPPA) is characterized by progressive disruption of semantic knowledge. This study aimed to compare the semantic features of words produced during a narrative speech in svPPA and the logopenic variant of PPA (lvPPA) and to explore their neuroanatomical correlates. Six patients with svPPA and sixteen with lvPPA underwent narrative speech tasks. For all the content words, a semantic depth index (SDI) was determined based on the taxonomic structure of a large lexical database. Study participants underwent an MRI examination. Cortical thickness measures were extracted according to the Desikan atlas. Correlations were computed between SDI and the thickness of cortical regions. Mean SDI was lower for svPPA than for lvPPA. Correlation analyses showed a positive association between the SDI and the cortical thickness of the bilateral temporal pole, parahippocampal and entorhinal cortices, and left middle and superior temporal cortices. Disruption of semantic knowledge observed in svPPA leads to the production of generic terms in narrative speech, and the SDI may be useful for quantifying the level of semantic impairment. The measure was associated with the cortical thickness of brain regions associated with semantic memory.