this is just my take....
southbeach/atkins are marketed towards weight loss and low "carb". there isn't a care what the carbs are comprised of as long as it is under a certain number and also allows for processed foods.
the primary goal of most ppl that do atkins/southbeach is weight loss (imho)
primal/paleo is for health and weight loss is just a bonus (for some...some ppl don't lose weight at all).
is based around whole, unprocessed, unrefined foods - healthy fats, veggies, meats, fruits. (most ppl associate primal/paleo with "no grains")
some ppl are eating this way to improve/control a condition/s, some are athletes, some to improve overall health, some just cuz they like it.
i think as far as the diff between paleo/primal or paleo/paleo depends on the person and what works for them/what they read first...some ppl eat dairy, some don't...some ppl eat nuts, some don't...some are hardcore organic/grass-fed/locally grown consumers and some eat what is affordable/readily available...some are low carb/starch and some are not, some count calories, some don't....for everyone (i will be corrected if i am wrong LOL) it is no processed foods, no grains, no refined sugars.