Soyuzmultfilm had a certain formula - a certain amount of time was given for so many minutes of animation. I think this length of time was more generous than for most Western cartoons, and was indicative of the different priorities - both sides tried to cut their costs (they both had only a certain amount of money to work with) and make films that people would want to watch, but in the USSR the emphasis was on the second (there was no point in making a film if people wouldn't watch it) while in the west the emphasis was on the first (there was no point in making a film if it was going to lose money).
A large function of animation throughout much of its early existence in the Soviet Union was to shape children into good adults - in essence, to do what parents should be doing. A lot of the films of the 1940s and 1950s were based on traditional morals - don't be selfish, help other people, get good marks in school. They're mostly very kind, good-natured films, and are beloved by Russians (and especially Russian parents) to this day. They provide quite a contrast from the Western films of the same period where animals are pushing each other off of cliffs and generally acting like jackasses.
Here's the thing: as I see it, both systems occasionally relied on swindling the viewer. The Soviet system "swindled" the viewer by making a great film and inserting a message into it that was beneficial to the government (see here for an example). That way, they (hopefully) had some influence on the viewer. But they had to make the film good; the better the film, the more likely the message was to be accepted. I should point out, though, that only between 1-5% of Soyuzmultfilm animated films were actually propaganda. Most were just children's films (with either no message or a with traditional, educational moral that most parents would agree with), and some were adult films (in the sense of being more mature in subject matter, not in today's sense of being pornographic). Even during WW2 (when the country was on the brink of being destroyed), slightly over half of the films were not propaganda but were based on fairy tales. Western studios like Disney and Warner Bros. also made a lot of propaganda films during that time.
The Western capitalist system, on the other hand, "swindles" the viewer by often making him pay more to see a film than the film is worth. It doesn't necessarily matter what people think of the film after they see it in this system - what matters is whether people will want to see it in the first place. Now, if the film is good, positive word-of-mouth can contribute to that. However, another way which is used quite often is to make a bad film but advertise it as being good. If enough people pay to see it before the bad word-of-mouth spreads, it doesn't matter anymore - the creators have already made a profit. In other words, it is a form of con artistry. Such a system can censor just as effectively as the more obvious censorship in the USSR - it hinders new ideas and puts more value on marketing and obvious "selling points" than on filmmaking skill.
In essence, the biggest difference was that in the communist system, the audience was guaranteed and the challenge was to make them like your film. In the capitalist system, the challenge is to make the audience want to see your film, and what they think after they've seen it isn't as important.
For a really interesting account of the differences between the communist and capitalist animation studios, I highly recommend reading this story. It's written by Gene Deitch, who went from an American animation studio to Czechoslovakia in 1959, and stayed there for a few decades.