Short answer: Private = potentially cheaper, less protection. Agent = professional standards, disclosure rules. Always get inspection and lawyer.
Private sales can be cheaper because there is no agent commission. But you have less protection. Agents must follow professional standards and disclosure rules. Private sellers might hide problems. Always get a building inspection and use a lawyer regardless of who sells.
Private Price: $580,000
Agent Price: $600,000
Private Risk: No professional oversight
Protection: Inspection + lawyer essential in both cases