I think it's just a personality thing. For me I have always wanted more than one and I actually think that it's as much of a choice as choosing between having no children and having any, because the end result is so different. (And of course, as with the first decision, you don't always get the choice that you wanted.)
I just have the one currently because I broke up with his father when he was one year old and then it's taken me four years to get to the point with somebody else where I want to marry them, let alone have more babies 
I feel quite sad that DS will never have that sibling close in age that I had wanted for him and I think we will end up having at least 2 more because I want to do the "multiple children" thing, and I don't think it will be quite the same with a big age gap.
From my experience with one and my observations of friends/talking to people both in RL and on here and my experience growing up with a sibling this is what I see as the differences:
With one child -
Relationship is more intense. Child tends to need your input a lot because you are their main playmate, especially if you don't have an extended family of cousins etc nearby. However, this also means that you have more time and resources to devote to them - for example, if your child loves trains you can spend a whole day at a specialist (read: very dull) transport museum without having to find childcare for the others, consider age-appropriate needs of others or have to drag around a trail of bored children. It also means that their interests often tend to be a little bit more adult, because you are so invested in them and spend so much time with them, you end up sharing your interests more with them which means there's a good chance they'll pick up on one or two of them.
You also have far more money and resources and it's easier to arrange things, so you have a lot more freedom. If you want to hop on a plane/bus/train for a weekend, you only have to find one extra fare, not two or three. Eating out, days out etc are cheaper because you're only paying for one extra person who usually costs less than an adult. Two children can cost more than one adult and three can cost more than two. It's not as difficult or stressful, nor does it require as much pre-planning, to keep track of one child in a crowded or unfamiliar place, so you're more likely to find the idea of a trip out less daunting (hence, again: more freedom)
But, the intensity can be a downside, especially if your child is extroverted. I struggle with DS' constant need for company and affirmation and I am an extrovert myself! It's hard when they are in the age of having very child-related interests like obsession over a TV show or something you find deathly dull, like, say, dinosaurs or playing sword-fighting games. I'd say this lasts from around age 2 or 3 to about age 7, so it's a long time.
With multiple children (again, not from direct personal experience, see above):
You have that variety in ages and stages. When your 5 year old is obsessing over the rainbow fairy books and you want to gouge your eyes out at the thought of reading one again, you have a baby or toddler to cheer you up again by doing something adorable or an 8 year old who wants help with their homework and you can help them to figure it out by themselves and watch them grow in confidence. When the baby is being grizzly, it's nice that the older ones are more independent and able to do stuff for themselves. etc. I would say that children who have siblings tend to be better at doing stuff for themselves in general too, because their parents don't have infinite time to help them and do things for them (no matter how hands off you are with an only, you can't get away from this really, and they pick up on it).
You feel like you know what you're doing a little bit (some days, I am totally convinced that this is the main reason people have more than one!) - but, I think there is an element of you've been there and you know how to deal with that stage and it doesn't feel as daunting as the first time when you had no idea.
They entertain each other. They can relate more easily to each other - especially in the small-child phase - much more easily than adults relate to a child. They are a friend to each other. They can look out for each other (to an extent) when you're out and about. You can get the older one to read the boring books to the little one OK, seriously, I know siblings fight and that is of course the flip side, but I was so close to my sister as a child and we spent hours and hours playing together. I love watching DS play with other children and I feel guilty that I can't play with him in the same way, or for as long, or as repetitively. I also love watching children together - I love listening to their conversations, seeing what things they come up with in their games, just seeing that bond and that relationship develop, I think it's magical. I think it's natural that they fight, so you do have to have some conflict management skills which aren't really as important when you only have one child.
I think that siblings are probably less dependent on their parents after they grow up and leave home, which again could be a positive or negative thing! It's a positive for me, because I have never wanted or expected to be the focus of my childrens' lives. Part of the appeal for me about having a family is seeing what interesting, independent, different people they turn out to be.
Mammoth post, but I think it's a whole different ballgame, no way is it the case that one is better than the other, it's just what suits you personally.