And the latter player is going to do this upgrade sooner or later.
The problem is that not everyone's plans revolve around upgrading to Swordsmen. I've played lots of games where I never had more than a couple Swords, if any, and it can work out very well to just focus on getting to Knights (or Cavalry) and getting as many of them upgraded as fast as possible. It's not better than an early Sword rush, or worse, it's map dependant.
A player who is saving up to upgrade to Knights (or Cavalry) may very well be in a 'better' situation than one who used their cash on Swords. That's something that varies game to game, and by playstyle. You can't have Knights in most cases in the QSC, but you can have Horses/Chariots and cash building up for them.
If a player upgrades to Swordsmen, there should be collateral points scored due to what those Swords accomplished. The Swords are worth more than the points they directly receive. Cities taken, leaders, promotions, ect. If they didn't accomplish anything (or failed to gain more than they lost), then they were a waste in the QSC period, and may very well be a waste for the rest of the game. If the upgrades were just done, then they are worth the same as Warrior+Gold under the rules.
it's more flexible to have already upgraded the warriors
Keeping your gold allows far more flexibility than investing it before being able to make use of that investment. If you have a use for the Swords, upgrade. If not, don't. Upgrading every unit is not always the best course of action.
I would say the 20 warriors and 1200g are worth more if everything else is equal, because everything else shouldn't be equal. The player who upgraded Swords should be scoring more from other sources (territory/pop) which they have aquired with their Swords.
Whether or not they are in a better or worse position depends on what both players are doing. If the player with the gold holds off and has a much better Knight rush because of it, they may very well overcome the Swords early advantage.
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I just don't agree that 1g is only worth half of a shield. I think it depends on the manner in which the player uses both, the goal the player has in the game, and in many cases is terrain dependant. There are some gameplay styles and game situations where gold is easily more important than production, others where it's only worth the shields it can buy/upgrade. I don't think it's fair to base it's value on one of the extremes.
A 1:1 ratio I think is fine, because the ratio is going to be variable, and it allows for the fact that gold or production could be the 'main ingredient' to success.