Will Venmo replace Western Union?

Most likely not.

Venmo is US concentric, whilst Western Union is available pretty much all around the globe. The problem that the two solve are inherently different.

It is very unlikely for Venmo to achieve a global status of what WU has. For that to happen, Venmo would have to become a household name like Western Union and also go into the business of assigning agents worldwide. 100,000s of agents. This is something I don’t see Venmo doing.