Comparing V'Ger and The Borg
In “The Motion Picture” Spock leaves the Enterprise in a thruster-pack space suit to explore V’Ger. On his journey, he saw a repository of worlds, planets, and galaxies V'Ger had encountered on its 300-year journey (including its home world) - inhabited by living machines. The Borg is a species ruled by logic and efficiency and it's unlikely that V'Ger and the Borg have any common origins because the Borg would never waste resources replicating hundreds of years of images of concurred worlds, planets, and vessels. Collecting images of past knowledge is the prime directive uniquely specific to V’Ger, not The Borg.
If V’Ger’s home world of living machines also happened to be part of the origins of the Borg, then why wouldn’t these same Borg-creating machines assimilate V’Ger as well? Instead, the living machines of V’Ger’s home world allowed it to continue (knowledge in tow) on its journey and mission back to Earth - rather than assimilate it as The Borg certainly would have.
There are some theories that The Borg was originally a humanoid species that possibly merged with a highly intelligent non-organic, non-human hive mind, at the molecular level. This Borg species trait of merging and assimilating is not part of V’Ger’s primary directive. Despite these differences, there are some similarities of note between V’Ger and The Borg.