Interview question: asset vs equity side DCF

Recently I got asket an interesting interview question for an internship at a European PE fund: in which cases would you use asset or equity side DCF? Which one do you think PE uses the most? As I was struggling to answer, the interviewer hinted that equity side would be better suited in a typical PE LBO to measure the IRR, which made a lot of sense to me. What you guys think a complete answer would look like?

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