As a person who have traveled to more than 6 different countries in the last 6 months, I can tell you which U.S. carriers are the best for getting data and voice overseas.
Many users have told me their 3G/4G LTE data network connection is broke after installing a custom ROM. Well, in most of these cases, it can easily be fixed by manually setting the APN (Access Point Name). This applies to any GSM networks such as AT&T or T-Mobile. For CDMA networks like Sprint or Verizon, they also use APNs but you don’t have to set them and should work out of the box.