Technically, at least given the terminology used in game theory, both are "auctions". What you probably think of a "standard" auction is known in academic circles as an "English auction". If by "tender", you mean sealed envelopes where the highest price is accepted, that is a sealed first-price auction. If the second-place bid is accepted, then that is a sealed-bid second-price auction or Vickrey auction. According to certain assumptions, every auction mode has the same expected sale price. As these conditions depend on the participants engaging in game-theoretically optimal strategy. In practice, psychological effects are an important factor, and different modes can have significantly different results.
The Vickrey auction has several arguments in favor of it. One is that it's in the prospective buyer's interest to be as honest as possible as to what price they would be willing to pay. It is arguably more efficient than an English auction; an English auction effectively is a drawn-out version of a Vickrey auction (the bidding continues as long the price is below the maximum price of at least two bidders, and stops once the price reaches the second highest maximum price). In addition, an English auction generally requires participants to be physically present, or at the least be active within a specific time frame and repeatedly submit bids. For a Vickrey auction, on the other hand, participants need make only one bid. The lower burden may attract more bidders. An English auction does, however, have the possible advantage to the seller of bidders getting caught up in a bidding war and bidding higher than they would if they had calmly evaluated the property's worth. In addition, there may be concerns in Vickrey auction of the seller taking advantage of the knowledge of the private bid.
A cursory search didn't turn up results comparing English versus Vickrey auctions in real estate, but I did find this result comparing English auctions to private negotiation, which found that the former resulting in higher prices, but only when there is significant interest in the property (after all, if only one person shows up to an auction, there isn't going to be much bidding).
Societal norms can also be an important factor. The above article notes that auctions are generally associated with distressed properties, but this is less true in Scotland and Australia.
Another article I found was this, which concludes that
... WTP information elicited through Vickrey auctions is undistorted by strategic behavior such as bid-sniping and incorporates the full range of WTP information, suggesting that it is better suited for estimating realistic price-demand functions for market research purposes.