Kaal Bhairava is basically the most popular form of Bhairava. However, Batuk Bhairava is actually worshipped more because of the energy.
The energy of Kaal Bhairava is highly intense, he is the adult form of Bhairava and is more fierce and aggressive in nature.
Batuk Bhairava on the other hand is the child like form of Bhairava, he is also intense but also has the innocence and playfulness.
Batuk Bhairava is considered as more approachable and he gives result faster being a small Bhairava. Kaal Bhairava is the big Bhairava, so he can be worshipped but it is advisable not to have his idol at home. He is the God of cremation grounds.
Batuk Bhairava on the other hand moves everywhere, he is the explorer, the one who wants to go everywhere. He travels along with Goddess Durga/Kali.
So in terms of energy, Kaal Bhairava is more aggressive and strict since he is the Kshetrapala, even Batuk Bhairava is easier to worship since he is playful.
ॐ भैरवाय नमः 🔱🙏