The answer is... it depends.
The little to no carb approach you mention is known as ketosis after the ketones produced by the liver when the body utilises fat stores for energy instead of carbohydrates and has been shown to be beneficial for a variety of things from fat loss to aiding focus and concentration to increasing life expectancy by cutting down the inflammation caused by carbohydrate intake.
People generally go high fat low / zero carb as a way to control calories as fat has 9 calories per gram, as opposed to the 4 per gram in protein, so if one increases fat, carbohydrates must decrease to avoid excess calorie intake (note: protein is very rarely decreased except for those with liver issues), but also because the body more easily converts carbohydrates to energy than fats, so eating too many will stop your liver producing ketones, knocking you out of ketosis.
The main issue with this approach is that if you're undertaking very intense, very frequent training (i.e. Crossfit style training daily), then the lack of carbohydrates in the body, combined with the stress of such high intensity training, can lead to decreased testosterone levels and higher cortisol levels as training stress accumulates.
The high carb low fat style of dieting is a bit of a throwback to the traditional bodybuilding style diet, and, I believe, was influenced somewhat by the mistaken belief that eating large amounts of dietary fat leads to heart disease (note: I say mistaken belief because, as usual, things aren't quite as clear cut, black and white as the media and marketing companies would have us believe).
Higher carbohydrate intake helps in recovery from intense training sessions, but, similar to following a keto diet and high intensity training, if dietary fat is too low, then testosterone and other androgen hormone production is impacted due to limited intake of dietary cholesterol.
So, it depends partially on your training.
The other thing to take into account, is the practicality of any diet / carb intake plan that you choose to follow.
Personally, I find it much easier to cook up a large batch of chilli and rice and take that to work as lunch for several days than I do to cook up something that has a high fat / low carb profile and keeps me full throughout the day.
Without knowing you, as a general recommendation, I'd say get enough protein (you can look up how much they're recommending this week, but it tends to be about 0.8g per lbs of bodyweight), and keep carbs / fats moderate.
Keep at that for 6 weeks and see how you're doing, then, if you think you need to, try shifting the carb / fat ratio up or down and see if it makes any difference.