You are not going to find these statistics. I put the evidence for this “below the fold.” Basically, crime stats experts all say that crime stats are unreliable before the mid-20th century.
However, I think private trips must have been robbed at much higher rates than commercial trips for the simple reason that the vast majority of highwaymen operated in the frontiers, where economic activity was overwhelmingly “private.” Read through Wikipedia's descriptions of American highwaymen, and you'll see that they mostly preyed on private travelers on isolated frontier roads.
According to Wikipedia's highwaymen list, the last New England highwaymen died in 1821. Well, New England (and the other developed coastal regions) are where the vast majority of the nation's commercial activity occurred. Banks didn't have that much incentive to be shuttling large shipments of gold across Illinois. If they did need to transport something as bulky as gold coast to coast, they'd take a boat. Because the majority of commercial traffic occurred in the safest parts of the country, commercial trips must have been, statistically speaking, very safe.
One wrinkle is that river pirates were probably more important than road agents/highwaymen. In an era of worthless paper currency, transportation is a major limitation to efficient robbery. Unless you are able to consistently target victims carrying high value-to-weight ratios (e.g. rich folk with pocket watches and diamond jewelry--unlikely on the frontier), you simply can't carry away much value after a robbery. It's also hard to make speedy getaway down backroads when weighed down with bulky item. Furthermore, how do you fence unusual stolen goods on the frontier? Even if you didn't have to worry about giving yourself away by constantly selling pocket watches, who on the frontier is paying top dollar for pocket watches?
The problem of transportation is likely why the most ambitious robbers were river pirates. Farmers are constantly drifting down waterways on rafts and boats loaded with valuable commodities. A pirate relieves them of their wheat, then floats downstream and sells it himself. This is much safer, because you can't prove that wheat once belonged to a particular farmer (like you can with a pocket watch), and you know that riverside towns are teeming with factors looking to purchase commodities.
Plus, river pirates were able to put greater distances between where they committed crimes, where they sold stolen goods, and where they lived. This was undoubtedly important--once again, read through the biographies of the highwaymen on Wikipedia, and you'll see that a significant portion of them were eventually routed by local posses.
PS- I know that 19th century bank robbers and train robbers have an outsized grip on the American imagination thanks to Westerns, but for the most part 19th century banking was very staid.
Why I do not think you'll find better statistics: I consulted my go-to source for questions like this (the Historical Statistics of the United States), and all I found was an essay that began with the following:
Three quarters of a century ago Edwin Sutherland flatly declared,
“statistics of crime are known as the most unreliable and the most
difficult of all statistics” (Sutherland 1924).
We face a “dark figure” of crime, where the number of unknown or
unknowable criminal events “haunts all attempts to estimate crime
rates even in the present; for the past it is multiplied enormously”
(Lane 1992, p. 39).
The only long-running crime statistics belong to New York, Philadelphia, and Boston, and those are not going include statistics on “road agents.” This is the most meaningful generalization the essay was willing to make on 19th century crime:
Fragmentary evidence suggests that the further south and west one
traveled and the more rural the district was, the higher was the rate
of murder (see Montell 1986; Vandal 1991, 1994; McKanna 1995; McGrath
1989). The record is even less clear for other crimes. Overall, the
severe limitations in crime data mean that it is very difficult to
generalize about crime in America as a whole before the middle of the
Here’s the limited semi-statistical information I was able to find on 19th century theft and robbery. From Lane’s “Urban Police and Crime in 19th Century America”
My guess as to theft is that there was then less than now. Certainly
this is true of theft from commercial places; when shops were small,
there was little display of abundance, no self-service, and much
careful scrutiny of goods and customers. The guess is less sure as to
theft from private persons and rests principally on the fact that
most people sim- ply had far fewer possessions of which to be robbed.
The great major- ity of reported thefts in the late nineteenth
century were of small consumer items, mostly clothing. Some forms of
theft, such as profes- sional pickpocketing, were then more common
than now, but outside of professionals it was not only the people who
stole who were often poor and fiercely in need but also the victims,
often neighbors, land- lords, or fellow boarders, who guarded what
they had with equal ferocity.
Robbery is very hard to call. In
nineteenth-century cities, robbery in the modern sense-that is armed
robbery-was quite rare, as noted earlier, so that, in one case, news
of a holdup in the Bronx ran in the Philadelphia papers for a week
(the New York cops blamed it on a person unknown but probably in town
with Buffalo Bill's Wild West troupe). Many other kinds of theft from
the person were, however, quite common: transient visitors to the
semisanctioned red-light district were liable to be rolled by
prostitutes or their confederates, and if they found it hard to tell
it to the judge next morning, the cases never got into the record
(Lane 1992: 43)