Hmm,well..it depends on the circumstances.here you should say ''I know''.

They mean the same thing in the context. Although I think the meaning of 'see' is closer to 'realise' than to 'understand' or 'know'.

Yes in the context of this phrase they all do hold the same meaning. Another verb that can be used here is "feel" which is often used in a more colloquial/slang context. To say you feel where someone is coming from implies that you empathize or can relate. When you say I see where you're coming from it means you understand it but not necessarily that you relate to it.