In addition to the overall shape of the antenna (length vs diameter), a big factor in creating deep nulls is the symmetry of the antenna, both physically and electrically. In addition the symmetry of the antenna's surroundings in the radio will come into play. Hence, a coil centered on its ferrite should (other factors equal) have better nulls than a non-centered coil.

An electrically balanced configuration will null better than an unbalanced configuration. The usual methods of achieving electrical balance involve differential amplifiers (common in some high-performance amplified antennas; not common inside portable radios) or using a balun transformer.

If the antenna and receiver circuit are "unbalanced", there are several factors that determine how much of an effect this has. A small (small overall ground plane and circuits) battery-powered portable can be electrically "floating" in its environment and still maintain some reasonable balance. Connecting a power adapter cord can drastically change the balance. Within the radio, the proximity of other circuits to the loopstick will influence the circuit balance.

Well, I've rambled on a bit, but this is an interesting and subtle question. If you wish to Google for more information, try searching for direction-finding antennas.

-Scott-