Those "characteristic" messages are all based on the IVs - they indicate which is the highest IV. In D/P/Pt (and Gen 3) when breeding, the baby will inherit three random IVs from either parent (i.e. choice from 12 total).
So, say you like the messages of both parent pokemon. There is a 3/12 chance the baby will inherit the highest IV from one parent, or 6/12 (50%) that it will inherit the highest IV from one or the other parent.
However, in HeartGold or SoulSilver, this is almost possible to control! If you hold an EV item, the baby will interhit that stat from the parent. Here's how:
1. Find which stat the message corresponds to from http://pokemondb.net/nature . So if you like "Often lost in thought" that's Special Attack.
2. Find the corresponding EV item. They are: Power Weight (HP), Power Bracer (Attack), Power Belt (Defense), Power Lens (Sp.Atk), Power Band (Sp.Def), Power Anklet (Speed). For the example it will be Power Lens.
3. Give that item to the pokemon with that message.
4. Breed it with another pokemon.
Now the baby will inherit the Special Attack IV. (It will also inherit two other random IVs from the parents).
Note: none of the above guarantees that the baby will have the same characteristic, because the other IVs are randomly generated and they could be higher. But you have a really good chance of keeping the same message.