The following is an excerpt from page 4 of the Warhammer Annual 2002 release with an expanded explanation by Gav Thorpe regarding the interaction between Character and unit Leadership and Psychology.
The combat abilities of characters may have been cut back, but that serves to emphasise their real strength as leaders of others. As most characters now have to rely on a bit of muscle around them rather than pelting off into the enemy at the first opportunity, their higher Leadership value plays more part than their fighting ability.
This is probably a good juncture to clarify a few points with regards to how characters interact with units. In particular, how characters and units with special rules for their Psychology and Leadership work with one another. On page 100 of the Warhammer rules you'll find a discussion of how characters interact with units with different Psychology liabilities. The upshot of this can be broken down into several simple principles:
Characters must obey all psychology-induced movement of the unit, as this is compulsory movement and a character cannot leave a unit suffering from compulsory movement.
As noted on page 100, characters gain no benefits from the Psychology of a unit they are in except if the unit they are in is immune to fear and/or terror, in which case they themselves are also immune (their bravery is bolstered by those around them). The same applies to panic - if the unit does not panic, the character does not either.
Conversely, characters never force a unit they are with to move with them (though they can if you wish). For example, a unit does not have to charge even if the character leading them is subject to frenzy. In this circumstance the character will be forced to leave the unit in the Movement phase. In the highly unlikely event that the unit and the character are subjected to two different compulsory movement effects, the compulsory movement of the unit takes precedence.
When it comes to Break tests, similar principles apply:
Only one Break test is ever taken by a unit - characters who have joined a unit never take a separate Break test. If the unit breaks, all models flee. If the unit stands, all the models stand.
Characters who are stubborn do not confer this ability on a unit they are with, though the unit may use the character's modified Leadership value as normal. Characters in a stubborn unit but who are not stubborn themselves allow the unit to either test on their own unmodified Leadership, or the character's modified Leadership, whichever is better (see page 85 of the Warhammer rulebook).
Characters who are Unbreakable must still flee if the unit flees, because the character cannot leave during compulsory movement. Similarly, characters in an Unbreakable unit will not flee because the unit must stay and fight (in effect they also become Unbreakable).
Now this last point can currently be used as a sort of back door way of making very powerful characters Unbreakable when really we don't want them to be at all. As we have been writing the army lists in the Warhammer Armies books, we have changed this. Since this is how it's going to be in the future, you might as well get ready and play using this rule now:
Unbreakable units cannot be joined by characters except those which are already Unbreakable. Swarms can never be joined by a character.