What are the reasons that a company would offer both qualified and
non-qualified retirement plans to their employees?
What is the best opportunity for a highly paid employee with a
publicly traded company - to use one or the other or both?

Companies offer both qualified and nonqualified plans when they want
their employees to be able to save as much as possible for retirement.
 As long as you do not need the money, participating in both types of
plans can be very attractive since you can defer as much money as you
want to while still contributing up to the maximum annual contribution
limit in a 401(k).

The only disadvantage to a nonqualified plan is that the future
payment to you is an unsecured debt, meaning that you are a general
creditor of the employer in the event of bankruptcy.  In contrast,
your contributions to a qualified retirement plan are supposed to be
held by a third-party trustee, which makes them safer.

Particularly as a highly compensated individual who is presumably in a
high tax bracket and does not need all of the money now, participating
in both types of plans allow you to delay paying taxes for a
potentially long period of time.  The tax-deferred compounding can be
extremely beneficial.

Sincerely,

Wonko

Source: "Non-qualified plans can create a retirement nest egg" by
Ginger Applegarth, MSN Money
http://moneycentral.msn.com/articles/retire/invest/1587.asp

Search Terms: qualified non-qualified retirement plan

Thanks - I understand it much better now.

For whatever reason, my last post was erased... but here's a bit more
info than Wonko gave:

Qualified plans do not allow tax deductions for employee
contributions, but they do often allow for deferred compensations (the
company can put money in this account instead of paying an employee,
allowing the employee to take the money out... thus pay taxes... while
in a lower tax bracket).
Unlike a qualified plan, an employer can choose to put money into one
employee's unqualified plan yet contribute nothing to another
employee's.

So in addition to the tax deferral of interest that Wonko mentioned,
the unqualified plan can be used as a way for employers to give
bonuses to high paid employees that will not be immediately taxed.