From my experience having done both low carbs and keto, I would highly recommend low carb.
As others have already stated, keto diet is high dietary fats, moderate protein and extremely low carbs, basically carbs coming only from some fibrous veggies. I did keto for about 6 weeks total on my last prep, it did work nicely for a little while but eventually the lack of carbs was causing too much brain fog for me and my training was suffering.
Essentially you start the keto diet, and within about a week or so your body starts producing more "ketones" and you'll use those for fuel instead of glucose. So you'll naturally start burning more body fat. The tricky thing can be you absolutely have to stick to the macro ratios because if you have too many carbs, even too much protein, you'll be "kicked out" of ketosis.
A low carb diet or carb cycling plan, just IMO, is best. I felt like crap when I trained on the keto diet.
You wrote you want to burn fat at a rapid rate, do you have a date or event in mind or are you just trying to get lean?
Another thing about keto is when you eventually transition out of it, you have to be very careful as you add carbs back in and your body gets used to them again.
The "optimal" diet for someone who wants to lose fat is one that creates a caloric deficit and one you can stick to, there's really not a lot of magic to it. Calculate your TDEE, start with a 10% caloric deficit and make sure you are sticking to your diet, training hard, and have at least 2 cardio conditioning days in your training plan.
Weight loss is very simple, you need to consume less calories than you burn. So, if you are "dieting" but you're not losing weight, then you're eating too many calories.
Be sure to post back with any questions!