Western Union was founded in 1851 in Rochester, New York as a telagraph company, and eventually moved from communications to money transfer. It is now based in Denver Colorado, and made $5.6 billion in 2018.

MoneyGram was founded in 1988 in Dallas, Texas as a subsidiary of Integrated Payments Systems. It was acquired in 1997 by Travelers Express Co which was established in 1940 and was itself acquired by The Grayhound Corporation, also known as Viad Corp, in 1965. It continues to have its headquarters in Dallas, Texas, and made $900 million in 2019.

While Open Assistant lacks the formatting capabilities needed to provide you with a table, here is a space-delimited comparison of the two companies' services:
Service             Wester Union                   Money Gram
Fees                  $4.99 - $149.99              $4.99 - $99.99
Exch. rate.        High                                  High
Speed               A few minutes to days     A few minutes to days
Limits                Vary by country               Vary by country
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