The seller's job is to sell the vehicle. Your job is to understand the vehicle, the numbers and the risk before you commit.
Dealer advantages
A dealership may offer more inventory in one place, financing options, trade-in handling, registration assistance, and a more standardized transaction process. Those conveniences can save time. The tradeoff is that the transaction may include dealer fees, optional products, financing offers, and a more structured sales process. You still need to evaluate the vehicle and the total cost.
Private-seller advantages
A private-party vehicle may have a simpler price discussion and sometimes lower overhead. You may also get more direct information from the person who actually drove and maintained the car. But you take on more responsibility for verifying ownership, liens, title status, required paperwork, condition, smog or inspection requirements, payment safety, and registration steps.
The seller type does not determine the car quality
A great private-party vehicle can be better than a poor dealer vehicle, and a good dealer vehicle can be far safer than a questionable private listing. Evaluate the specific vehicle rather than assuming one source is always better.
Choose based on total risk and total cost
Compare the car, inspection results, history, transaction protections, financing, paperwork burden, fees, and your own comfort level. The best source is the one that gives you the right vehicle at a price and risk level that make sense.
Bottom line
Do not let urgency replace verification. Compare the market, understand the history, inspect when appropriate, review the complete transaction and decide your maximum before emotion takes over.