Low Fat or Low Carb

Neither is necessary. A calorie deficit will cut fat, a slight calorie surplus will build muscle.
Protein is for muscles.

If you are going to concentrate on any macro, i would suggest protein. Ideally, you should be aiming for .8g to 1g of protein per lb of lean body mass. Other research would suggest .35 to .6g of fat per lb of lean body mass and the rest carbs.

But all of this is contingent on training routines and which type of diet will help you stay in a deficit.

Neither, people assume I eat low carb because I don't eat much bread/pasta/grains. I do this because I tend to over indulge on those foods and they are calorie dense.
I get my carbs mainly from fruit and veg, and I try to eat more "good" fats like avocado, raw olive oil and coconut oil, nuts and yogurt.
In the end, low calorie is the way to go, how you get there is up to personal preference.

Low carb (per my doc, severe PCOS and insulin resistance) is easier for ME to create a calorie deficit while feeling full and not deprived. However, whatever you do should be sustainable long term, which is difficult for some people with low carb.

If the only choice is low fat vs low carb

Low carb wins hands down. Don't believe me, research peer reviewed articles on the subject.

But dieting is mostly about calories in vs calories expended.

Neither. I need moderation of carbs and fat to keep me going.

I think It's interesting that people say they don't do 'low carb' but cut out many major sources of carbs (pasta, rice, sugar, ect) Effectively that is low(er) carb. Why such a stigma with low carb diets? There are many ways to restrict your eating habits, vegetarian, vegan, no red meat, ect... Low carb is just one of those ways.

Personally I used to be in the group that thought restricting carbs was silly, I used to think that it was all hogwash and eating carbs had nothing to do with health, it was all calorie counting.
I feel differently now since experimenting with low carb eating, I tried ketosis, and while that works and is beneficial to some, I personally don't have the self-control required at this time to maintain ketosis. I keep my carb levels low, haven't been tracking lately but I feel best when I do not eat bread, pasta, rice, beans or sugar.

My foods are any type of meats, good fats, (coconut oil, olive) any dairy, plain yogurt ect, usually whole fat and any veggies and fruits. Occasionally I will have oatmeal or starches, sometimes even crackers or a cookie. I'm not a carb restriction fanatic.
BUT the biggest change that I LOVE is how my body feels. After going low carb I realized how much water I retain when eating a high carb diet, my ankles and calves were always swollen, only after being low carb did I notice a change. Before that I was unaware of the effect. I feel lighter, my muscles ache less, I get better sleep and my brain functions more quickly. I have tested this by going on and off low carb many times since I began this journey. I always can't wait to start eating low carb again, because the way I feel is amazing.
For weight loss, no matter if you are low or high carb calorie count still matters, low carb isn't a license to stuff your face and forget about a deficit, although I can attest that you will still stay unswollen even if you go over you calorie deficit... LOL

In short, don't hesitate to try low carb if you think it may help you! I support it fully.

I completely agree with starryskies. My body loves low carb...I feel so good, alert and full of energy, no digestive issues and I never feel like I'm starving.

Limit carbs to around 100 and sugars to as low as you can and you will lose weight by the fistfuls. I'm down 24 pounds of fat and 43 to 35 inch waist in the last year. I added 5 pounds of muscle.