Two people are holding either end of a couch, is one person exerting more force than the other?

I believe the following diagram tells you everything you need to know: when the center of mass is above the support point, then the lower point will carry more of the weight since it is acting closer to the center of mass ($x_1 < x_2$) and torque balance requires that $F_1 x_1 = F_2 x_2$. Conversely, if the center of mass is below the support, the higher point will carry more of the weight when the object is tilted.

Understanding this diagram really helps when you are moving large objects up or down the stairs: the lower person should grab the object higher up (say the arms of the couch) if you want to achieve more equal weight distribution.

ADDENDUM

In the second case, if the person on the right pushes against the couch, it is possible for the person on the left to end up carrying the entire weight of the couch. In the case of carrying things up stairs that can easily happen... Which is why movers often use webbing straps to permit/ensure a more equal distribution of effort (and to allow lifting with shoulders/back/knees and not just arms).

Although Floris made a clear picture involving only vertical forces, this picture is mostly useful when carrying washing machines or large chairs, where the 'height' of the object is more pronounced.

However, you will find that, even when the object is mostly flat, the bottom person will carry most of the weight. The key here is the direction of the forces involved.

You will find that it's very difficult to lift a couch underneath you, 'tugging' it upwards. Instead, the top person will apply force in the direction that does not require any tugging (especially when you can't get a grip): perpendicular to the object. All you do, is offset the torque gravity incurs on the couch, where we take the bottom person as the pivot point. In the image above, the torque is provided by the component of gravity perpendicular to the couch (green arrow).

Since the top person is twice as far away from the pivot point as the center of gravity, he will only need to apply half of that component which was already less than the total gravity - i.e., much less than half of the total gravitational force. The top person has the easy job, although usually in a very awkward position.

The bottom person needs to account for the rest of the upward force required, along with a small horizontal component to make sure there is no horizontal acceleration (blue arrows) - i.e., a lot more, which is why being the bottom person is the heavier job.