This debate has been skewed for decades by propaganda produced by proponents of a variety of food industries, mostly in America.
For example, the sugar industry paid Harvard scientists to publish a 1967 review of research on sugar, fat and heart disease. The studies used in the review were handpicked by them, and the article, which was published in the prestigious New England Journal of Medicine, minimised the link between sugar and heart health and cast aspersions on the role of saturated fat.
The makers of butter and margarine also had their own pseudo scientific bun fight in the states and so the debate on whether saturated fats contribute more to heart disease than unsaturated fats rages on with studies piling up evidence (some more scientifically credible than others) on both sides of the argument. The fact that many people fail to consider the role of sugar in heart health at all means that the sugar industry have been extremely successful in influencing public opinion!
One result of 50 or 60 years of bad press against saturated fat rich foods like butter is that the food industry has been able to grow fat (if you'll excuse the pun) by creating hundreds of low fat (so called) diet foods which are loaded with salt and sugar.
Similarly, the cholesterol theory of cardiovascular disease is thought to have been given undue credence due to studies published by scientists in the pay of agents of the food industry and as a result "cholesterol lowering" yogurt drinks and margarine have been making someone very rich while normal people have been shying away from the humble and, by and large harmless, chicken egg for fear it will literally kill them.
In the present day the press is increasingly reporting on a global obesity epidemic which is widely thought to have been as the direct result of people consuming too much refined sugar so the truth is coming out at last. It's only a shame that so many people had to get type 2 diabetes beforehand.
So the bottom line? Science has been hijacked for the nefarious ends of people who want to make a lot of money out of their products and no one has really been in the picture for 50 years, least of all the government who are lobbied by the food industry and still roll out The Eat-Well Plate as the model balance of food groups (Hint: it isn't).
In reality, a calorie is a calorie. If you consume too many, no matter their source you will gain weight (consuming fat is not the only way to gain body fat) and consuming too much fat or sugar will have health consequences. No one nutrient can take the blame for all our woes. Let's bring proteins into the the ring for a moment... Diets too high in protein can cause high blood pressure and give you kidney stones so clearly protein is not blameless either!
In answer to the question above, neither is the enemy. The enemy are the unscrupulous food industry who want you to buy their products and are not above creating questionable scientific studies to influence your purchasing decisions.
Buns don't kill people, people do.