Note that in all cases losses include not just elements that have been destroyed, but those that have been lost for any reason, including moving off the table, being ensorcelled or fleeing the field. Elements such as lurkers which have fled the field, destroyed hordes and ensorcelled heroes or magicians count as lost until they are brought back. Once brought back they no longer count as lost.
A player's army is worth 24 points (AP). Each player scores points equal to:
Enemy AP Lost + Own original AP - Own AP losses
A player that has lost the game is assumed to have lost all 24AP, regardless of actual casualties. If the scores are calculated correctly then they should add up to 48.
Example: A player captures the enemy stronghold to win the game, having lost 4AP of troops in the process. The winner gets 24 (Loser's full army value) + 24 (Own army value) - 4 (Own losses) = 44 points. The loser gets 4 (Killed enemy elements) + 24 (Own army value) - 24 (Own losses) = 4 points.
In the event of a drawn game scores are calculated as normal; they will be 24 - Own losses + Enemy losses.
Ties are broken by the number of enemy general's elements killed.
This system provides a good spread of scores making ties unlikely, but the arithmetic confuses some players (the idea that scores must add up to 48 helps eas this a little). It does heavily penalise losing, making cautiously not losing (even if by playing for a draw) more attractive than a win big or lose big strategy. This can have a tendency to encourage overly defensive play or agreed draws.
This is the same as Berkeley scoring, but penalises draws. A draw is only worth:
Own losses - Enemy losses.
This makes draws very unattractive, but in doing so penalises those that were due to a hard-fought game timing out. Those innocent of cautious or slow play are punished along with the guilty.
Both players score the value of enemy elements that are lost. The winning player also scores a 12 point bonus.
The downside of this scoring system is that it penalises those players who don't win by slaughtering the enemy army. It is possible to win by scoring low numbers of casualties on the enemy army (capturing the stronghold, for example), but the scores favour those who win by destroying half or more of the enemy army. It does not directly penalise players for their own losses, however, so encourages a more aggressive style of play.
A win scores 2 points and a draw 1 point. Record own AP lost and Enemy AP lost; ties are broken by the player who has the best AP loss differential.
This system makes ties for places more likely, especially over a small number of games. The tie-break system suffers from the same problems as the Minnesota system, in that it does not reward players who kill enemy generals or capture strongholds as highly as those who destroy enemy armies. On the plus side it is easy for players to record their scores.
Modified Recon Scoring
A win scores 2 points and a draw 1 point. Record Enemy AP destroyed; ties are broken by the player who has killed the most enemy AP.
This has the simplicity of the Recon system, but the tie-breaks reward aggressive play. Note that if you win a game your own losses are irrelevant.
New Berkeley Scoring
A win scores 3 points and a draw 1 point. Record Enemy AP destroyed; ties are broken by the player who has killed the most enemy AP.
Again this has the simplicity of the Recon system, but wins are more heavily rewarded.
It is impossible to come up with a scoring system that is fair in all circumstances, and tournament organisers must decide which kinds of behaviours they should reward. I think there is a majority who seek to 'penalise' draws, encouraging both players to play for a win in the allotted time. The problems come in using systems which score based on element kills, as these penalise players who win by killing enemy generals or capture a Stronghold. Against that are systems which don't take into account killed or lost elements; they fail to distinguish between a lucky player who wins by killing the enemy general in the first combat and one who, thorough skill and tactics destroys a high proportion of the enemy army with little loss to themselves.
And, of course, any scoring system must be easy for the players to use and for the organisers to assess.
Thoughts are welcome in the comments, as are alternative scoring systems not covered above.