Atkins for me every time because it works.
Everybody I know who's tried it (and didn't cheat) lost shed loads of weight. I lost a couple of stones too. Given it up now though cos it is boring after a couple of months.
The health scares are absolute rubbish. The whole 'conventional' diet industry have been searching the world for people suffering health problems from Atkins and they found one person who 'Might' have suffered as a consequence. Tens of millions are on the diet so I think its worth the 'risk'.
The risk arguments are usually based on the 'low fat diet' opinion that if you stuff yourselves with high fat food it will clog your arteries and give you a heart attack. The reverse is true though - on Atkins you are actually losing the fat in your body and therefore improving your health.
Years ago a diet involved cutting out bread, potatoes, cakes and sweets (ask your parents, grandparents). In the seventies the 'low fat' industry started. Suddenly whole meal bread and jacket potatoes became the staple healthy option. The 'low fat' diet, loaded with carbohydrates, does not work so the portions sizes have to be reduced and you struggle, feeling hungry all the time.
As I see it, Atkins is just back to the common sense beliefs of our ancestors who learned what worked and what didn't. All Atkins did was explain scientifically and physiologically why such an approach worked.