Is it better to operate abroad as a local entity or as a U.S.-registered company?

Very subjective question. The answer would be, it depends on the country in question. Each country has its own pluses/minuses when it comes down to doing business within their borders.

Some countries have it very easy for you to setup as a foreign business and be able to repatriate your profits. Some are just the opposite. Some work in between, they will let you setup, but repatriation of funds is not an easy venture.

Double-Taxation is also something you need to look at, and see if the two countries have a taxation treaty. You can get hit by corporate taxes, taxes on repatriation of profits and then taxes in your own host country.

Registration as a foreign entity vs local entity can best be decided upon after talking to the Tax and Incorporation specialists in both countries.