Rhonda, it sounds like you've answered your own question. The bottom line when choosing a long-term plan is that it must be something you can stick with long-term. If getting your protein sources from low fat dairy products, soy products and egg whites isn't something you can live with long-term, then Pritikin and Ornish probably aren't the plans for you. Just like Atkins (or any other controlled carb plan), these are plans you are expected to stick with for life, not just until you get the results you wanted and then you can go back to your old eating habits.
OTOH, following Atkins doesn't mean that you have to eat all the saturated fat you can find. If the thought of saturated fat bothers you, choose fish, chicken, turkey, lean pork, whole eggs and leaner cuts of beef and fattier cuts of meat only occasionally and leave out the bacon and sausage. Use smaller amounts of salad dressings, butter and cheese. Use olive oil for cooking and add flax oil to your salads.
I personally don't believe that saturated fat is harmful when following a controlled carb plan, but there is no law that says you have to eat a lot of it on low carb to follow low carb correctly.