A typical double cheeseburger is going to be loaded with saturated fat, both from the beef and also from the cheese. If the cheeseburger uses lean beef and low-fat cheese, it may contain much less. Granted, if "typical double cheeseburger" means something from a typical fast food place, chances are the beef won't be lean and the cheese won't be low-fat. Some people also are suspicious of beef and cheese because of hormones and antibiotics given to cattle. I myself try to find hormone/antibiotic-free beef/dairy products although I nevertheless don't get too worked up about it either way. Beef and dairy fat also may contain small amounts of trans-fat, but it is conjugated trans-fat and does not have to be considered trans-fat for nutritional labeling purposes. Also, from what I understand, naturally occurring animal trans-fat is not unhealthy in the same way trans-fat in hydrogenated products is. So, a cheeseburger could normally be considered free of bad trans-fats if it were just beef and cheese and a decent bun, but last time I checked, McD's cheeseburgers had small amounts of bad trans-fats in them. I'm not exactly sure why. Maybe their buns are baked with some hydrogenated oil in them.
Chinese fast-food can vary a lot. It really depends on the place. The two big concerns, at least as I see, are trans-fat and high sugar content. Some Chinese places fry their food in hydrogenated oil, which makes their food high in trans-fat. I'd totally avoid that. But many Chinese places don't use trans-fat containing oil, and often they'll be clear about that. That doesn't exactly make it healthy, but I do think it makes the difference between something one shouldn't eat everyday and something one should never eat. Also, many Asian sauces are full of sugar and/or corn syrup. It makes the food nice and sweet, but it does boost the amount of calories without raising the level of nutrition.
So, with both foods, I think it depends, but neither cheeseburgers nor Chinese fast food are the sorts of food you should be eating constantly. And I think with both foods, if you are able to pick out the ingredients at the supermarket yourself and cook them yourself, you can have more control over how healthy or unhealthy they might be.