Chatbot or live chat?
The comparison is not bot against human. It is a bot against a live chat widget nobody is currently watching.
Which is better, live chat or a chatbot?
Live chat, whenever somebody is genuinely available to answer within a minute or two. A chat widget with nobody behind it is worse than no widget, because it invites a question and then ignores it.
What should a small business chatbot actually do?
Answer questions it has real facts for, capture the enquiry, and say plainly when it does not know. It should not attempt to sell or improvise around gaps.
The failure mode is a bot that answers everything confidently. One invented answer about price or availability costs more than the widget earned all month.
Can you run both?
Yes, and it is usually the right shape: a person during hours, software outside them, with everything landing in the same place so nothing is answered twice or missed.