All of the Dragons' personalities are inversely proportional to those of the wishes that created them (whether they were selfish or selfless). They also bear a direct relation to their time in the manga (comical or dark). Their power levels are also directly proportional to the strength of the wishes used to give them life.
Haze Shenron is the weakest and most comical of the Shadow Dragons, and is correpondingly created by a wish that takes place in the the early half of Dragon Ball (specifically, the Fortuneteller Baba Saga), a very comical anime in and of itself. The wish that creates him revives only one person (Bora), and so the wish uses relatively little power, leading Haze to be the weakest of the Shadow Dragons.
Rage Shenron is individually frail, but has some of the deadliest elemental powers of any Shadow Dragon, and is created by the wish that revives Goku after he sacrifices himself to kill Raditz (only one person is affected directly, but it is designed to save everyone from the Saiyans). Rage Shenron's powers of Elasticity is strong enough to withstand Goku's 10x Kamehameha, even though his offensive power is not even enough to hurt SS4 Goku at all. Rage is relatively dark compared to Haze or Oceanus, but is created in Dragon Ball Z, which is considered a much darker anime than Dragon Ball.
Oceanus Shenron is the second most comical dragon, and is created in a time when the series is still very comical (specifically, the Emperor Pilaf Saga). She is both good (in that she provides free fish to the townsfolk, and it was only they, not Oceanus, who abused their newfound laziness, though she may have counted on this) and bad (in that she uses several dirty tactics to try to defeat Goku and pollutes the town with rotten fish), and is created with a wish neither completely good, nor completely evil: Oolong wished for a hot girl's panties (or the most comfortable underwear in the world in the dubbed version), which may also explain why Oceanus has a female appearance. However, as Oolong made a selfish wish with good intentions (wasting the dragon's powers before Pilaf could wish for world domination), Oceanus is likewise an evil dragon beneath a benevolent facade (both figuratively and literally, as she also hides her hideous true form behind her elegant "water spirit" persona).
Naturon Shenron is the darkest of the first four dragons, and is created in a very dark time in Dragon Ball Z. He uses very evil tactics (such as using Pan as a human shield), which corresponds to the selfless wish to revive Majin Vegeta's victims in the Majin Buu Saga. Incidentally, Naturon is very weak until he possesses a body, at which point his power rises exponentially. This parallels Majin Vegeta's "controller", Babidi, who was likewise a relatively frail schemer who relied on others to defend him.
Nuova Shenron is created by King Piccolo's wish for eternal youth, which is undeniably selfish, and as such, is the most noble and honorable of the Shadow Dragons. Nuova is also notable for being the fastest among the dragons; his speed is enough to completely outclass that of a Super Saiyan 4, and catch even Omega Shenron by surprise. He is very serious, as the King Piccolo Saga is a very dark and serious time in the Dragon Ball anime.
Eis Shenron is among the dirtiest of all the Shadow Dragons, even more so than Syn Shenron (he uses both Pan and Nuova as shields to protect himself). He is created by a wish that is made so that, of all people, Majin Buu, a creature responsible for the deaths of billions and the destruction of countless planets, could have a second chance by making everyone but the Z Fighters forget their evil deeds, arguably making it the most selfless wish made.
Syn Shenron is created by the wish that most likely revived the most victims, since one can only reasonably assume that others besides the Namekians were killed by Frieza and his henchmen in the preceding year. Therefore, just as Haze (being created by a single person's revival) is the weakest, Syn (created by the most people's revival) is the strongest. His brutal, unrelentingly evil nature could be the result of the amount of negative energy used to create him, or as a result of the selflessness of the wish's intentions (by reviving the Namekians, the heroes intended to use Porunga to transport everyone except Frieza away from the dying planet of Namek, leaving the tyrant to perish in the explosion).