I think it's a YMMV (your mileage may vary) kind of thing. I've been doing this on/off (more on) since the late 90's, and I shift into ketosis and lose best when I count total carbs and try to keep it at 20 grams (the old Atkins Induction levels). That being said, if I exceed 20 and it's because of good, green leafies, I don't sweat it.

When I try to count net carbs, I find myself bargaining and consuming faux foods (bars, low carb replacements, etc.), subtracting sugar alcohols and any other little tricks I've heard about recently to make my carb count seem better. Doesn't work for me. Best for me to keep to fats and meats w/ some veggies thrown in as I crave them. I'm currently keeping things low on the total carb front for a few weeks until I'm firmly planted in Keto land again, and will slowly increase veggies and occasionally low carb fruit
until I'm consistently in the 20-30 gram (total) range.

My body really likes to be in ketosis, so the quicker I shift gears and reach that state, the better for me. Using this approach I'm usually testing dark purple on my ketostix within 24-48 hours. Ketostix may not be the most precise indicator, but it worked for me when I started Atkins in '98 and it's a good enough tool for me now. ;-)

I stick to total carbs, but I also don't eat "lo-carb" pre-packaged food items(currently anyway), so my carbs all come from dairy/veg(leafy and cruciferous) so it's not that hard.

FAQ's and guides about keto should all officially say to use net carbs I believe, but be smart about it. Eat your veggies and for the most part you're good there (with green ones typically, others have a bit more sugar in them), but be wary of "artificial" type products that tell you they have 30g carbs but only 2g net. If you're new to keto I'd absolutely stay away from those things, and the Atkins brand products I'd probably stay away from forever, most of them use Malitol which is really really crappy. Once you're keto adapted if you want to experiment with things like that to learn how your body reacts go for it.

Personally I use net carbs, because I feel better when I get my fiber in, via veggies and chia seeds. So my goal is just 20 net carbs, and ~25g fiber a day, so I'm getting 35-45g "total" carbs a day, but technically my goal is 20g net or less at all times.

Just a note, lots of carb counts you find on the internet when you look up a food...are already net carbs...they've already done the calculations for you. That grinds my gears. I also do old school carb counting.

I don't think it's been specifically said but,

Net Carbs = Total Carbs - Fiber - Sugar Alcohols (if any)

Atkins is the only place I really see the Net Carb limits stressed. The Atkins products are completely gimmicky and go against everything I think Atkins himself ever intended. I won't touch the Atkins shakes, but I do usually keep the EAS carb control shakes on hand for the convenience. They truly are only 2 net carbs with 5 total (3 fiber and no sugar alcohols).