There is a difference between rodent species, and choosing the one that you think is cutest or prettiest may not be the best choice for you as a pet.  I wouldn't say any of the rodents are "better" or "worse" as pets (although I've already revealed my bias towards rats!), but rather that they make better or worse pets in different situations, with different people.  The problem is choosing which one best suits you!
 
Rodent Species:
• Rats
• Mice
• Hamsters
• Gerbils

 
There is of course more; chinchillas and Guinea pigs are also rodents, however, I'm only including the smaller ones.
 
There's also less common, less available species, that you may not have even heard of!  Some of these are Degus, Duprasi, and Dormice; each of which are as different as the above species, with slightly different care and personalities.  The main downside to all of these is their unavailability; you simply may not be able to find them for sale.  Also, they cost more (around $15 on up to $40 or $50 or even more apiece, depending on where you live and their availability in the are).  The only one of these that I've kept are the Degus; here's My Experiances with them.
 
Some things to consider when choosing a species:
• What kind of personality do you prefer?  Would you be happy with a less "interactive" pet or do you want one that will be affectionate and friendly?
• How much time are you willing to devote?  To remain tame (and in the case of rats, friendly), a certain amount of time must be spent with them; this does vary by species at least to a certain degree.
• How much space are you willing to devote?  Different species require differently sized cages.
• Will this be a pet for the kids?  How old are the kids, and how good are they with animals?  Some species are more skittish, more likely to squeeze out of small hands, or more likely to bite.
• How many rodents do you want to keep?  Most prefer company, but not all.
• Do you want to breed them... How much extra time and space do you want to devote to this, and how many youngsters do you want to deal with?

 
Comparisons:
• Personality:
• Of course, varies by individual as well as species; however, there's a few generalizations -
• Gerbils: Very active... *very* active!  Always doing something, exploring something... *chewing* something.  Except when they're sleeping, which tends to be done in short naps throughout the day.  They're probably the friendliest of the smaller rodents ("smaller rodents" defined as all but rats), and they often like to be held, if only so that they have new territory to explore!
• Hamsters:  Probably the calmest, and, if I do say so myself, the dullest of the bunch.  They're nocturnal and tend to spend much of the day sleeping.  They're not too horribly friendly, but once they're tame they're easily held simply because they're not as quick.
• Mice: Like gerbils, they tend to be active and curious; though they're a bit less hyper and a bit calmer.  They're nocturnal, but not to the degree that hamsters are; they will spend periods during the day active.
• Rats: Always my personal favorite, for one simple reason that makes them different from all the other; they're *friendly*.  They like you, very genuinely; they don't just like being out of the cage, they like *you*.  They're very affectionate; they love being scratched behing their ears, and they're lick you in return.  They purr when happy and will play-wrestle with your hand (especially as youngsters).  Real sweethearts!
 
• Time required:
• Gerbils: Need a certain amount of time spent taming them, and to remain tame.  About average.
• Hamsters: Need quite a bit of time spent taming them; once tame, they need only a minimal amount of time to keep them tame.
• Mice: Rather like hamsters.
• Rats: Rats are practically born "tame", and most youngster even having never been handled will be as "tame" as any of the other rodents; however, to reach their full potential of friendliness they need time spent with them, quite a bit at first; how much time spent with them relates directly to how friendly they become.  Once very tame, however, they tend to remain so even without much handling.  Though, of course, that's no way to enjoy your wonderfully affectionte pet!
 
• Space required:
• Gerbils: Mid-range... a pair or family does well in a 10 gallon tank sized cage, but the more space and the more toys (the more stuff to explore!), the better.
• Hamsters: Mid-range; a single animal does fine in a 10 gallon tank sized cage, or a bit smaller if you're pressed for space.  If they're to be kept in pairs or more, they require considerably more space; otherwise, when they have arguments, the loser will have no place to run.
• Mice: Minimal space required; a pair can be kept in something as small as a five gallon tank, although of course, the more space, the better.
• Rats: Require the most space, because they're considerably larger.  A 10 gallon tank sized cage would be the absolute minimum for a pair of smaller rats, and that's only if they got to spend a good amount of time out of the cage everyday.  A better cage for a pair would be at least 14" x 24".
 
• How they do with kids:
• Gerbils: Okay.  Not the best, not the worst.  They're active enough that younger kid require adult supervision with them, unless you want loose gerbils!  They do sometimes nip, however most gerbils only do just that; nip, and rather gently.  There are a few individuals who actually bite.
• Hamsters: Again, okay.  They're much calmer than gerbils or mice (once they're tame), and so are less likely to be lost.  However, they tend to be harder to catch once lost than gerbils (because of their nocturnal activities and less exploratory attitudes; they'll likely just find a comfy hole and fall asleep, whereas a gerbil will want to explore everything, and hence make itself visible).  They do sometimes bite, especially before they've been well-tamed, or if they're woken up in the middle of the day.
• Mice: Bad in that they're *very* easy to loose; they squeeze easily out of small hands, and have the speed of gerbils combined with the nocturnal activities of hamsters.  However, they rarely if ever bite, and even if they do bite it's much less gruesome because the animal is so small.  I've only been bitten a couple times; all totally my fault, and none drew more than a little tiny bit of blood.
• Rats: My personal favorite for kids; first, they're bigger; even small hands can hold them easily.  They're less fragile; squeezing that could kill a mouse won't even phase a rat.  Same goes for dropping.  They're calmer; most will sit happily in small hands.  They never bite... I qualify this statement by saying that there is the rare individual that will bite, but if you get one of these, take it back and get another one; *most* individuals will never bite, the exceptions being when a rat is protecting a newly-born litter (some rats do this, some don't) or when a rat is in extreme pain.  And last but not least, if they *are* dropped or set on the floor - the same instances any of the other rodents, especially the hamsters and mice, would go shooting with unbelievable speed to the nearest dark corner that they'll be impossible to extract from - in the same instances, a rat will sit calmly on the floor and sniff.  Even if they do wander off, they'll more than likely wander right back to you a few minutes later!  Or back to their cage; they're big homebodies!
 
• Do they need company?
• Gerbils: Yes; should be kept in pairs or more.
• Hamsters: NO.  No, no, no.  Do not keep hamsters in pairs, especially not female hamsters.  They will fight, and they will quite possibly kill each other (yes, I've seen it happen).  Some people have had success keeping hamsters in pairs (especially with male brothers), but in most instances it simply isn't worth trying.
• Mice: Yes, should be kept in pairs or more.
• Rats: Should be kept in pairs or more; some people like to keep single rats thinking that they will be friendlier this way, however this isn't really true (a pair will be just as friendly just so long as you spend time with them), and a single animal will get lonely when you're not right there with it.  So unless you're going to be with it 24 hrs a day, I suggest you get a pair or more!
 
• Breeding Introductions:
• Gerbils; are the least prolific of the bunch, a plus rather than a minus in nearly all cases - you don't have to deal with as many babies.  Males and females get along great, and the males help out with the care of the babies.  1-8 babies, 2-6 average.
• Hamsters; the most difficult to breed, in that you can only introduce the male and female very carefully or your male is going to end up injured!  1-18 babies, around 10 average?  I'm not exactly a hamster breeder...
• Mice; way too easy to breed.  Need I say more?  Males and females can be kept together, the one problem being the female will be receptive to mating within 12 hrs or so of giving birth; she will become pregnant again!  1-16 babies, around 8 average.
• Rats - rather like mice!  1-18 babies (yes, I've known a rat that gave birth to 1 baby, and I've also known a rat that gave birth to 18!), 8-12 average.
 
Anyway, that's a quick introduction to some of the differences between the species; bear in mind that's just an introduction!  Choose a species that interests you and *research* it!
 
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