Is hard to tell just like that. You can do some research online. Look up what searchers are currently entering into their queries, what does google give as possible search options... Do people search more as a conversation word1 and word2 ? Or without the and?
For online sharing purposes you might want a shorter domain but that shouldn't stop you from going with the longer one because you can get "shortlinks" created for Twitter and such, also length is not an issue if you share clickable links that don't have to be retyped by your potential visitor.
Your domain had to be SEO friendly... But also not an issue at the beginning, regardless of domain you will have to do a lot of SEO and marketing work to build relevance online so Google shows you in queries that don't include your direct domain name...
My suggestion: If your product or brand will be mentioned out loud or read a lot to include the AND then include that in your domain..
It's usually better to go with the shorter version if possible, for the sake of making it easy for people to type in. However, if it's a branding issue then the longer one. If people know you as "frank and oak" then that's better to go with frankandoak.com verses frankoak.com. If the second redirects to the first, you win no matter what.
Barnes & Noble uses BarnesAndNoble.com. But they also forward BarnesNoble.com (without the "and") to their website. Beyond that, they ALSO own Books.com / Book.com and forward that pair to the full brand name: BarnesAndNoble.com.
There may be cases when shaving off the "and" is justifiable. But it's dangerous to give specific advice when we've been given no specifics!
I'm lost. Should I go North or South? Well, that depends where you are and where you're trying to go.
Depends on the words. Rolls Royce fit together nicely. Johnson and Johnson need the and. How customers, clients and management say it on the phone and in public is far more important than SEO comments below since that can always be fixed