Here’s a great chart comparing the various diets that are sensitive to “Low Sugar” and “Ancestral eating”
Low Carb is pretty straightforward and promoted through the popular Akins diet. However, the criticism towards this diet usually comes from the SOURCES that the food is obtained namely “Processed ” food sources.
The Paleo diet attempts to look at historial patterns that human/hunter gathers used in their food choices. Criticisms here seem to be some of the practically of eating this way and particularly the avoiding of DAIRY.
Lastly , the WAPF diet named after Weston A Price
seems to address the dairy needs of a diet and its role in the body. This counters the Paleo (SISSON) approach.