That’s one of those quotes kind of like, “What happens in Vegas
stays in Vegas.”  It works great as long as everyone buys in completely
and conducts themselves accordingly.  It’s helpful to separate
friendship from business on several levels, but especially so when your
business will be competing head to head with that of a friend.  The key
to success in such an arrangement is to be open and honest and talk
about how things are going to go.  You can even set a few ground rules
if you want (although fewer is probably better than more.  The more
“rules” you have the greater the likelihood one of you will break one
or more of them and cause a rift.)

The best thing you can do is say, “We’re going to compete head to
head.  I will deal with you, your company, and my / your / our clients
in an open and honest way. “  It’s important that both you and your
friend understand that someone is going to win and someone is going to
lose.  But that certainly doesn’t mean you have to cease being friends.

I remember my son playing on the high school baseball team.  He
competed against all the teams in the valley.  Then, after high school
ball was over, the American Legion Baseball season started up.  Of
course the American Legion team drew players from all over the valley. 
So one minute they were “mortal enemies,” and the next they were best
friends (and teammates.)  I noticed that even though they were
competitors during the high school season, they were still cordial to
each other.  It wasn’t uncommon to hear, “nice hit, Bob,” or something
like that.  Make no mistake, each team was playing to win.  And each
was giving their all, no matter who was at bat or on base.  But the
fact that they were competing didn’t get in the way of being friends. 
You could be happy when your friend did well and vice versa without
affecting your desire to come out winner at the end.

It’s like that in business.  Competing doesn’t have to mean we’re
not friends (unless you decide it does.)  As for me, I know we’re both
going to do our best.  We’re not going to cheat, or do anything
underhanded, but we’re going to compete to the full extent of our
talents and abilities.  At the end of the day, someone’s going to win
and someone’s going to lose.  But if we don’t sacrifice our honesty and
integrity to “win at all costs,” when it’s all over, we’re going to go
out for dinner together, congratulate each other, and move on to the
next thing.  Because after all, friends are friends and business is
business.