The main difference is that each has a different interpretation of what a true paleolithic diet would be.
Primal by AV emphasizes low carb, high fat, high protein and low fiber, and includes plenty of dairy. It's very high in meat, eggs, dairy, green vegetable juices, coconut cream, moderate honey, and occasional fruits and nuts. It also encourages small amounts of fermented foods.
Typical paleo is high in sugar, high in fiber and moderate in fat and protein. With tons of fruits, a moderate amount of meats, some vegetables, some eggs, some nuts, occasional honey, and excludes dairy. Generally discourages juices and fermented foods.
The main criticism of primal by typical paleo adherents and others is that dairy probably wouldn't have been consumed by adults in the paleolithic era.
The main criticism of typical paleo by primal adherents and others is that fruits were rarely available except when in season, and in any case they wouldn't have been nearly as sweet as modern domesticated fruits.