Some sellers don't know the law. Some think that by using a ffl the automatic background check will get them off the hook if you do something later which proves to get the LEO or BATF involved. Many FFL s will want a fee from you and the seller to run it through his books then you must pay state sales taxes if he runs it through his books because if he get audited for sales taxes he will be held liable for not collecting and remitting that sales tax to them. Had a ffl friend who owed a lot of money because he did not collect sales taxes on just these type transactions. State said the fact he made only the transfer fee did not mean he did not have to collect sales taxes. They pointed out if he sold a gun at a loss he would still have to collect taxes so the fact he made zero on the gun was irreverent.
So it comes down to more than one ffl fee. Be honest with yourself. Few guns are going to be worth this amount of hassle and extra expense. When in doubt just keep looking another gun will be along shortly. Private sales are fine unless they get more complex than they are worth.