There are four levels of literacy/illiteracy: can't write name; can write name but not much else; can read some but can't write; can read and write. Every literate society has examples of each category, so we are attempting to assess the levels of each. The federal censuses before 1880 asked questions about literacy, but the information is spotty, so it is not of much use. That means we have to rely on anecdotal information rather than statistical, so we are back to where we started, namely, that we already knew every society had each category and what would be nice to know is relative levels. That's what you're asking and it would be great to know, but it's not an easy question to answer.

To unravel all of this a few thoughts: the West was one of the most international places on the continent. The gold and silver rushes attracted international attention and consequently there were people from throughout the world. Even if they could read their own language, they were no doubt slower to read English, which doesn't always look much like it sounds. Certainly many of the places that sent its sons and daughters did not have high level of literacy, so we can suspect that a higher percentage of these new arrivals were not literate in any language.

I was able to review the oldest records created after the 1859 gold and silver strike that established the Comstock Lode, home to Virginia City, soon to be of the Nevada territory (I was the first historian to review the document after Eliot Lord looked at it in the early 1880s). This was a record of land and claim purchases and exchanges dating back to June 1859, days after the strike. A single transaction involving James "Old Virginny" Finney (for whom Virginia City was named) revealed his name with the following: "His Mark X". This tells us several things. First he was so illiterate that he couldn't write his name. No one knew this until I found that evidence since his illiteracy is not otherwise mentioned in the primary records. That also means that other people who wander about in the primary records could have been illiterate and we wouldn't necessarily know it. This book of transactions also tells us, however, that everyone else could at least write their own names. That doesn't mean that they could read - or write - other things. And we have to keep in mind that the people in that book were the ones who owned, sold, and/or purchased property, so they were on the upper rungs of the ladder. These conclusions don't tell us much about the rest of society, but it does hint that a majority of the people who arrived "from the States" could read.

We also get a hint of literacy rates in the 1880 census, which describes what children were doing. For those between around 5 and 15 in the Nevada census, "At School" was the designation for well over 90 percent of the children. We all know that attending school does not necessarily mean literacy, but this is an amazingly high rate of school attendance: people wanted their children to be educated, and newspapers lovingly described every new school erected.

And that brings us to one more piece of evidence, namely, the newspapers. The newspapers of the West were all the rage. They were popular, they spawned rivals that attacked one another, they voiced opinions, and people treated all this as a form of entertainment. One of the first things a new settlement did was to establish a newspaper, and primary source records describe rare newspapers from "the States" being passed around so everyone could lap up news. There were those who no doubt did not participate in all of this, but the way newspapers and their editors and reporters were so thoroughly integrated into the fabric of society tells us a lot about how many people were reading what was written.

Of course, that's like evaluating modern society by the literacy rates of the people who look in on /r/AskHistorians: 100 percent of those who visit here are literate at least to some degree, but that doesn't tell us much about the rest of society, and so we return to the original question and its unknowable answer, namely relative rates. My instinct tells me it was relatively high, but there is no real way to prove it.

Source: I discuss a lot of this in my book The Roar and the Silence: A History of Virginia City and the Comstock Lode (1998).

edited to provide link for Eliot Lord.