At our club tonight the following position occurred:
Black, an inexperienced player, did not wish to trade queens, and so played 1...Qa6?? allowing 2.Qg7#
We know the tactical consequences of allowing 2.Qg7# are far worse than the strategic consequences of not trading queens when ahead.
But let's change the issue and ask "From an instructional standpoint, is it worse that Black refused to trade queens when winning or is it worse that he overlooked a mate in one?" Your opinion on this question can't be wrong so long as it's your honest opinion!
In an article for Chess Life over a decade ago, IM Jeremy Silman argued that, from an instructional standpoint, it is clearly worse to fail to make a favorable trade of queens when you are winning than it is to put your queen en prise or miss your opponent's checkmate in one.
I agreed with him, and wrote a Novice Nook to this effect: Accidental and Purposeful Errors (http://www.chesscafe.com/text/heisman97.pdf).
The gist of the argument is that anyone can make a mistake, and for an instructor to point out to a player rated ~1000 "You should not miss that your opponent is threatening mate nor allow your opponent to checkmate you" is not telling him anything he did not know. The instructor can discuss advantages and methods to taking your time, being careful, asking "What are ALL the things my opponent's last move does?", and developing board vision and tactical vision to spot these threats; however, telling him that allowing checkmate is bad is not news nor very helpful.
On the other hand, failing to trade into a winning endgame (or its cousin, purposely and unnecessarily trading into a losing endgame) is something that is only done by volition. I normally make the analogy that a player who consistently refuses to trade pieces when ahead in material is like a football coach who tells the scorekeeper not to run the clock when his team is ahead. You don't win many games that way!
An absolute beginner might not know this, but a player at Black level should know better. He can't claim that he "accidentally" played 1...Qa6, failing to trade queens. He can claim he didn't see 2.Qg7# and we should all believe him; that was an accident, and accidents happen. But when you don't do as you are taught (like follow the strong principle "Normally when you are ahead material, you should trade pieces but not necessarily pawns") then reasons like "I did not want to trade queens - I wanted to threaten 2...Qxc4+" are open to legitimate constructive criticism. You don't always trade queens when you are ahead in material (it's a principle, not a rule), but you normally learn to Walk Before You Can Run (http://www.chesscafe.com/text/heisman116.pdf).