Migrate all database tables with the following prefixes

cbsubs_
comprofiler_
groupjive_

Next migrate the following folders.

/administrator/components/com_comprofiler
/components/com_comprofiler
/images/comprofiler

There's several other folders pertaining to Joomla plugins and Joomla modules that you can either just re-install or migrate them from their respective Joomla folders. Core CB does have Joomla plugins and modules though so usually it's best to just install CB over the top of it self once done to cover those or you'll need to move those as well from their respective Joomla folders.

That migrates basically 99% of CB. The main issue is the following Joomla tables that we depend on.

_users
_user_usergroup_map
_usergroups
_viewlevels

You'll need to be sure you handle those as well otherwise your users won't exist in Joomla and any usergroup/viewaccesslevel settings would be broken.

1.  I take it it's best to install the base CB and any other plugins onto the other site first and then migrate (and potentially) override tables.

Yes, typically it's a good idea to have a blank template of what you want. So basically install CB and any plugins you normally would want. Then migrate the data. Doing it this way you only need to migrate the /images/comprofiler folder to move stored files.

2. What about on a site that already had some form of setup already vs a clean base install?   Is that asking for trouble?

You'd need to be careful about overriding existing data. Typically this is a nightmare waiting to happen though if you have already registered users as you'll cause a cascading problem of conflicting user ids. For example what do you need if the user id 30 exists on both sites? Big problem to have.

3. If I have done an extensive amount of language overrides, are the table you noted looking after that part as well?

Language overrides are entirely file based. My language override block post below shows where they are. You'd need to migrate those yourself.

www.joomlapolis.com/blog/kyle/18701-language-overrides-have-arrived

For example default language overrides would be in the following folder.

/components/com_comprofiler/plugin/language/default_language

So I would not have to migrate these tables? 

You will if you're moving data from 1 site to another.

or these folders?

You don't need to migrate those folders if you've installed a clean CB with the plugins you intend to use already.

Right, I had not thought about that.  If users already exist could be a nightmare.   I think I am most concerned about just migrating things like the CBSubs plans, CB setup and any other plug setup like Groups, Mailer, etc.

If you're not migrating the user data then you don't need to migrate _comprofiler for example which contains user data. There's several others you could probably exclude. I suggest checking your database and deciding for yourself what you may or may not need. Many plugins configurations are stored in _comprofiler_plugins in their params column so it maybe best to just move their params column data instead of the entire row so you don't break plugin ids.

Maybe in the future we'll provide some sort of tool to help with this, but for now you need to be well versed in SQL and the database structure mainly.