For all the circles people go round and round about different diets, the health profile improvement of weight loss for obese people is gonna completely outweigh (haha) any possible risks most of these diets may have, practically speaking if the diet works for them.
My understanding of low-carb vs low-fat is that yeah some health markers (e.g. LDL) on low-carb can be worse in the short-term, but the weight-loss and some other markers also tends to be better short-term. Long-term, it actually ends up being about equal. So whichever one works for you.
Realistically speaking, if we're talking about satiety though, it's not about low-fat or low-carb, it's about high protein.