Rats tend to be cheaper (in care, initial cost, etc.) than chinchillas, so even if I wasn't horribly biased towards rats, there is a big factor right there. The big drawback to rats is their short lifespan.
Since I've never personally owned chinchillas, I'll just talk about rats. One of the most endearing things about them to me, is how different in personality each rat is. I've never owned the same rat twice, if you will. My first rat probably remains the closest to my heart. He was a shy creature hard of sight. It took me over a month to gain his trust (I found ketchup, while unhealthy, to be an invaluable tool with him). It was like a light switch when he suddenly trusted. He was like a completely different rat, and bruxed (rat purr, if you will) and boggled for hours, loved to be pet. Another dear rat was a wily female. She hopped on and off the couch at will (only rat I've had brave enough to do so), would come when called, followed me around the house, and had a HUGE crush on my husband. She would scare the pants off of him leaping halfway across the room onto his lap and stand up begging til he swung her. Some rats fetch, some cuddle, some lick (especially the dumbos it seems), some groom you, some learn tricks, some teach themselves, some are shy, some are bold, some are picky about who they like, some are social. But, they do tend to have something in common. I have never met another animal so consistently upbeat and loving.
The two genders tend to have different traits. Females often have softer fur and are more slim. They tend to dribble pee a bit more, and are more active and playful. They also, unfortunately, tend to develop mammary tumors. Males tend to be more chill, more nippy in their cage, more cuddly outside of it. They tend to be lap rats. Their coat is often coarser, and they can be a bit mustier. So long as you stay away from oranges, they usually do not develop tumors. My males usually do not dribble urine. I love both genders as pets. I am staying away from more females until I can find a line less prone to tumors. Too sad to deal with for me.
Another awesome thing about rats is that you can get them as adults, and in a group, and if you spend time with them, they'll still bond strongly to you. I've had adults bond to me more than rats I raised from youth. If getting females, get at least two. Males can do fine in pairs or groups, but I have seen males seriously injure or kill a cagemate after peacefully coexisting for years. Females will often barber themselves and be obviously stressed when kept singly. I've never seen a male do that though, and most seem fine if alone...if they get tons of human time. Most rats are happier with other rats around though. They are very social, and some can become pretty neurotic or overly timid when kept alone.
Plus, they look about as different as they act. There are rats of every color, mini rats, longhaired rats, nude rats, rats with ears set low, tailless rats (not big on those because they use their tails for balance and for temperature regulation), and rats with curled whiskers and fur. In short, rats are awesome. I'll probably never be without at least one.