I keep ing reading about the two different services to travel through Italy. Which is the better service to use and less costly to an AMerican traveling in Italy?
There's no such thing as a Eurail service through Italy. Eurail is a type of rail pass. The train system in Italy is primarily Trenitalia. There are also several smaller local and regional train systems in Italy. All depends where you are traveling. Most train journeys in Italy can be seen on www.trenitalia.com. Importantly, they can be seen, but not purchased, on the great German train website www.bahn.de.
As for the Eurail pass, it covers you completely on all Regionale trains in Italy. But, it doesn't cover you fully on Intercity or any of the nicer high-speed trains. You will need to pay a supplemental fee on any train requiring a seat reservation. These are the Intercity and high-speed trains. When you purchase tickets in Italy or online from Trenitalia, you get the seat reservations automatically. No so with the Eurail pass. 3Euro extra for the Intercity train and 10Euro for each high-speed Freccia train. You can buy the seat reservation at any train station in Italy or you can do this online as well. Usually, the Eurail pass is not cost-effective in Italy.
I think you were thinking of the Italo Train which is an alternative to Trenitalia. You can look up the Italo schedules here: http://www.italotreno.it/EN/Pages/default.aspx. Italo is a newer, private line competing with the government run Trenitalia. The fares are about the same. Italo in some cities uses a different train station. Reports I have read (no personal experience) is that the service is better on Italo. Italo only runs high speed express trains. You can do a web search and find several comparisons to make your own conclusion.
Have used both trenitalia and the new company italo. Used italo on 2 trips to Italy in 2013 booking in advance through their easy to navigate website. Was very pleased with italo.
The only thing to note with Italo is that it does not use the "main" stations in Rome and Milan (Roma Termini and Milano Centrale). If you are making a connection to a smaller city, Trenitalia can be more direct. I have not used Italo so I have no personal experience, but from some things I've read they seem about equal.
I've ridden all the 3 varieties of Freccia - Bianca, old rolling stock barely upgraded but going faster; Argento, pretty good and smoother; Rossa, quite nice and comfy but spoiled for us on a nonstop (!!) Rome-Milan by three coaches full of school kids.
The Italo is pure pleasure, leather seats - IMHO better than anything Freccia has - runs on time mostly, the off stations that they are forced to use by the state monopoly have very nice WIFI enabled lounges for use by all passengers, and they have a free movie car at the end of the train and free WIFI throughout the train (although with the mountains and tunnels not always perfect).
The prices can be quite similar, but given a choice I will take Italo every time.