Hi Derek,

One of the abbey's you mentioned had the answer on their web site.

Question: What's the difference between an abbey and an archabbey?

Answer: "Abbey," "monastery" and "priory" are roughly synonymous terms.
A monastery generally refers to the building where the monks live. An abbey is
a monastery governed by an abbot, while a priory is a monastery ruled by a prior under the auspices of the abbot of the mother abbey.

The title "Archabbey" was given by Pope Pius XII to Saint Meinrad during its centennial in 1954 to honor Saint Meinrad for its role in the development of the Swiss-American Congregation of Benedictine monasteries in the U.S. There are only 11 archabbeys in the world.

As you said, the other archabbey in the United States, is St. Vincent's in Latrobe, Pennsylvania.

Here are the two in the United States and their web sites:

• St. Meinrad in St. Meinrad, Indiana
• St. Vincent in Latrobe, Pennsylvania
  

Providentially, I found a blog that listed all eleven archabbeys:

Romish Popery — Dedicated to all the Popes, past and present.

1. Montecassino, Italy
2. Monte Oliveto Maggiore, Italy
3. Arpino (nuns), Italy
4. Beuron, Germany
5. Sankt Ottilien, Germany
6. Brevnov, Czech Republic
7. St. Peter's in Salzburg, Austria
8. Pannonhalma, Hungary
9. Saint Vincent, Latrobe, Pennsylvania, USA
10. Saint Meinrad, Saint Meinrad, Indiana, USA
11. St. Sebastion, Salvador (Bahia), Brazil
    

You said:

• Does anybody know why they are "arches," and why we only have the two?

The prefix arch means principle or chief so in the eyes of the Swiss-American Congregation of Benedictine monasteries, they would be considered their principle monasteries.

• Why we only have the two of them in the United States?
  

I don't dare speak for the head of the Swiss-American Congregation of Benedictines.
I'm a spiritual Benedictine myself : )

Mike