Both take place in Rome; they just take place several thousand years apart from each other. Fellini-Satyricon takes place in ancient Rome, whereas La dolce vita takes place in modern-day Rome. Both La dolce vita and Fellini-Satyricon are essentially plotless; they are just people moving through life. That is the most obvious connection. In La dolce vita the main character is despicable, because he cheats on his fiancée all the time . He is despicable, but that is the end of their relationship; they break up after that. He still seems to be sort of human; he is not the most evil person in the world. In Fellini-Satyricon the main character is pretty much the worst. There is a scene where there is a person who is said to be the child of a god but is just really an albino person who can barely walk or move and is cared for by an old blind man. So, for money, they decide to kill the old blind man and steal the not god person, and then through neglect she dies.
Another similarity between La doce vita and Fellini-Satyricon is that, in both the main characters are failed writers trying to deal with themselves. Both of the main characters go to an almost never-ending realm of parties and feel disconnected from the world. Both films end with the main characters giving up writing and becoming rich people, but not really getting that much out of that. In a sense, both movies somewhat hold the same plot - they both lose a lover. They are in a lot of ways the same movie, just one is a weird insane movie that takes place in Rome, and the other one is generally a much more down to earth film. Fellini-Satyricon is the crazy one that doesn't make any sense and is totally fragmented, although in an interesting way. Also, in Fellini-Satyricon there is homosexual sex whereas in La dolce vita it is mostly heterosexual.
There is some surrealness in La dolce vita, but it is a relatively down to earth film; there is nothing in it that could not actually happen. It is just basically a guy gets drunk and doesn't feel totally connected to the world. On the other hand, Fellini-Satyricon is madness at every corner. Fundamentally though, they are about similar things. They are about feeling alienation in the modern world – in each one what is modern at the time. Definitely one can see that they are made by the same filmmaker.