Ammunition is still definitely inflated in price; even with the current market (fears over 'assault weapon' bans and the like), a normal round isn't going over a dollar per, and it's 20 nuyen for 10 normal rounds currently. That doesn't even get into the cost for flechettes/buckshot.
The economy is vastly different as well, so it's hard to judge. The US has been carved up like a turkey, so while Seattle may be a trade hub, anything traveling by truck or rail has to pass through a couple of countries to get delivered, and some of those have well armed or hostile borders. Not to mention that ammo is cheap only when it's not being used.
I think the best metric to compare the value of the dollar is the cost of a moderate lifestyle - ¥5000 - to what the cost of living is for a single person living a middle class life style in Seattle today. I'm ballparking based on a website from a quick google search, but they suggested to use 2/3 the median income as the lower limit for middle class. In 2012, the median income was approx $88000, making 2/3 about $58700 - just a hair less than the yearly cost of a middle class lifestyle in shadowrun - ¥60000. A person living paycheck to paycheck could still afford all the amenities of a middle class lifestyle without generating any surplus. That seems to be a good baseline for the price of a lifestyle, anyway.
So based on that conjecture, I'm going to say that $1.00 is approximately ¥1.00. Any fluctuations from today's prices represent scarcity, demand, or other economic factors driving the prices up or down. Makes me wonder what the cellphone plan is for a Fairlight Caliban (shudder).