If you are eating carbs, high intensity cardio will, in my opinion, burn just as much fat as low intensity. Although high intensity cardio seems to inhibit fatty-acid mobilization and metabolism during actual exercise, it seems to cause a massive post-exercise fatty-acid mobilization. Basically, you burn carbs during high intensity cardio and burn more fat later on because of it. For about an hour after some high intensity cardio, your body is metabolizing fat to replenish intra-muscular triglycerides and other recuperate.
If you are in ketosis, you are not eating very many carbs. High intensity cardio *requires* glucose/glycogen because of the muscle fiber type used. This means that you should not do high intensity cardio while in ketosis --- your body will catabolize a lot of muscle in the process of obtaining glucose from amino acids and glycerol (cortisol and glucagon). This will not happen as much with low intensity cardio in ketosis, because you will be using mostly type 1 (oxidative) muscle fibers that can more easily burn fatty acids.
Likewise, if you are in ketosis for a long time and try to lift weights with very low muscle glycogen, you will be weak and lose lots of muscle. Your muscles rely almost exclusively on glycogen while lifting, so you will be weak. Your muscles *cannot* use ketones for energy. Your type 2 fibers (ones you use most for lifting) have a very difficult time utilizing fatty-acids. Lifting will make your muscles even hungrier for glucose (thereby lowering your blood-sugar and causing cortisol and glucagon release), and gluconeogenesis (cortisol and glucagon) will eat your muscles. This is why a non-stop ketogenic diet will destroy your muscles. A cyclical ketogenic diet will allow you to train because of temporarily elevated glycogen levels.