I've done them both...successfully. So this is what I would say:
Low carb is a great way to help you to deal with cravings as it naturally diminishes your appetite. It also is nice perk that you really don't have to be near as strict with watching sodium as high protein, low carb diet works naturally as a diuretic. Fried foods, ribs, chicken skin, etc. and all while losing a ton of weight...what's more to say?
Ok...now the down side of low carb - it's unsustainable for many. AND...if you don't transition correctly (which very few people actually do), then you WILL gain back all the weight +
Calorie counting - I prefer this method as it teaches moderation right off the get-go! Additionally, you can have any food you like, you just have to watch your portions and monitor your daily calorie intake. If done correctly, I believe this is the most effective method long term.
