Both exist here, and the right choice is per item.
When an auction earns more
When you do not know the price. Which is most of the time for anything not uniform. The room finds it.
When there is competition. Two interested people produce a number neither would have offered alone.
When the item is interesting. An auction is an event. A fixed price is a transaction.
When condition varies. The room prices the specific example in front of it, which a fixed price cannot.
When a fixed price earns more
When you know the price and it is fair. Nothing is gained by discovering a number you already have.
When you have several of the same thing. Auctioning identical units one after another drains a room — the second sells for less than the first and the fifth for much less. Managing stock.
When the audience is thin. A quiet auction is a cheap sale. A fixed price does not care who is watching.
When the buyer wants certainty. Some people will pay a premium not to compete for something.
The mixed show
The approach most experienced sellers converge on: auction the interesting things, fix the price on the repeatable ones, and use the auctions to hold the room while the fixed-price items sell quietly alongside.
What not to do
Do not set a high starting price because you want a high price. That is what a reserve is for, and starting high instead is how an item gets no bids and then looks unwanted.
More: setting a starting price.