They also offer, at a discount to their customers, rental World phones if you don't have a phone that uses the EU system.
As far as the US, Consumer Reports rates Verizon's system number 1 in 29 out of 30 of the biggest markets.
My own experience — I drive some 100,000 miles a year all over the US, and have never lost service on the road with Verizon....how many can say that with ATT, Sprint, etc. For example, I check with people on a golf course in major cities who have NO service with others while I have four bars.
Now, and for many year, I've USED them all. I am always asking — in restaurants, gas stations, etc. — people on other systems who are on the road. NO ONE has the near coast to coast connectivity I have.
I’m very glad that your experience with Verizon was better than mine. I found them duplicitous.