Step 1: The classification of vasculitis hinges on the dominant vessel size affected, which guides the answer.
Step 2: The three large-vessel entities to remember are Takayasu arteritis, giant cell (temporal) arteritis, and Cogan syndrome. Three of the four listed options fall into this category.
Step 3: Churg-Strauss syndrome, by contrast, is an eosinophil-rich, ANCA-associated process that targets small vessels and is associated with asthma and eosinophilia. It does not fit the large-vessel group.
Step 4: Therefore the entity that is not a large vessel vasculitis is Churg-Strauss syndrome.
\[\boxed{\text{Churg-Strauss syndrome}}\]