Are Vyrso books tagged exactly like Logos books or are they sort of tagged? Also, are they tagged to all other resources that are in ones library, whether they be Vyrso bought or Logos bought?
No. :-)
Bible references are actually, but they have the possibility of being incorrect: Logos runs an automated processor on the publisher-provided book files that tries to find and automatically tag Bible references, but it's not perfect. Other than that, they are not tagged.
Do you think that Vyrso will eventually marry with the Logos processor in the future so both will be fully searchable and taggable?
Vyrso books are fully searchable.
Logos books are manually tagged by humans, and they are maintained and updated by Logos which is why they cost more. Vyrso books are the plain ebooks direct from the publisher without any intervention from Logos employees. That's what makes them different. Vyrso books will always be something less than Logos books. They are basically the same as Kindle books with added Bible verse tagging.