Well, let's start with 3 Estates, 7 Coppers, 1 Silver and 1 Smithy and say you draw to $7 on T3 after playing Smithy, exactly 7 Coppers in hand.
Now let's take Smithy in consideration, here my math will get wonky.
With Gold, you have a deck of 13 cards, but you do have Smithy, so you can have a hand of 5 regular cards and another of 5, one of which is Smithy that draws the last 3. So effectively you have a 2 hand deck.
With the Coppers -> Silvers, you end up with 11 cards, but it takes less than 2 hands to go through them, starting with a Smithy hand (5 + 3 = 8 cards seen), you have just 3 cards left that we can count as 3/5th hand; it's probably slightly more since you can redraw the Smithy in this hand and go through faster.
Gold: $7 + $2 + $3 = $12 per 2 hands = $6 / hand
2 Silvers - 2 Coppers: $5 + $6 = $11 per 1 3/5 hands = $6.875 / hand
This gives a significant edge to the Silvers.
Still, taking into account Smithy makes the math wonky, so I hope I didn't make any glaring mistakes. But the gist is that a smaller deck is just worth it to rapidly increase spending power per hand.
Actually Smithy hands do not change expectations here. It is pretty straightforward to calc one Smithy.
Ignoring Smithy, you average card has $9/11 in buying power on T3. On a non-Smithy hand you then expect $45/11 or $4.09 per hand. That happens in 7/12 hands. Smithy hands happen 5/12, Smithy is worth 3 * average coin/card or 7*9/11 = $5.73. The weighted average then is $4.09*7/12+$5.73*5/12 = $4.77 per hand on average.
Adding a Gold makes it exactly $1/card (12/12)
Trashing two Coppers makes it $1/card (11/11)
For the Gold, 8/13 hands will not have a Smithy. 5/13 will. This means that our average hand is 40/13+35/13 = 75/13 or $5.77
For the Silvers 7/12 hands will not have a Smithy. 5/12 Will 35/12+35/12 = 70/12 = $5.83.
The big value here, up until you green or are junked, is that the Silvers move the whole deck faster thanks to needing one fewer card. As Davio noted, being 1/5th of a hand faster is pretty nice per shuffle, particularly given the breakpoints of the early game.
The other thing here is that your odds of crunching the Estates are better with the Silvers. Odds that Estates show up in your Smithy hand are higher thanks to having one fewer card competing for slots. Remember there is no rule that you can only Trade once, so you need to also consider how much faster you will get to the big payout hands - and trashing the Estates to silver is pretty massively huge.
Think back to when we all had to learn the power of Jack -> engine. Jack is a beast precisely because it replaces Estates with Silvers, you want to do that with Trade and do it ASAP. And lest we forget, the variance is not all that terribly important when you are looking at high $5.X hands; Gold is much more likely to give you huge payouts ... which is pretty inefficient if you are buying gold at $7 anyways. It would have to be a very odd game to make the Gold option better.