I have an iPhone 6s with Verizon. I’ve been given an iPhone 6plus in better condition by a family member that used a different carrier. The iPhone is unlocked and rest. Will I have any problems transferIng side by side

Sorry, missed your statement. You need to check with Verizon first and see if this iPhone will be accepted on their system. If both phones are running the same version of iOS 13 yes you will be able to do a quick setup. Make sure the family member follows this: What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

As is often the case, the devil is in the details.

Specifically, which network the 6plus was used on.

Because different carriers use different cellular technologies and different radio wavelengths, it isn't possible to say that any phone will work on any carrier - Apple built different iPhone 6x's for different carriers.

It's a little dated now (due to the age of the iPhone 6 and changes in the cellular service industry), but this link has a good walkthrough of the options. You may be able to use this to determine if the phone will work.

https://www.whistleout.com/CellPhones/Guides/Will-my-iPhone-6-6Plus-work-on-another-carrier

The good news is that there's little risk - if it doesn't work you can just revert to your old phone.

Is this also a Verizon used iPhone? Are both on the same version of iOS?