Yes, these sentences basically mean the same. I would think the first sentence is more of a recommendation, while the second sentence is more of a command.

The first one can mean, as others have said, that it is you for whom it is important. The second can mean that it is the job to be done that is important, whether it is you or someone else who does it.

Very similar

They can mean quite different things or have subtle differences. It's important for you to do it - when a person says this to you, he/she is saying that "it" is important, you should do it. He might mean that it's probably going to be for your own good if you do it, compared to not doing it. It's important that you do it - this sentence may be the one that is said when it's not only you who is involved in the situation. For example, if there are two of you who can volunteer as a teacher in an outreach program, and a third person talks to you, telling you that you should do it (he thinks it will be better you do it compared to the other person) Essentially, these two sentences compared, the first one talks about you doing it or not, the second one is more of "will you do it or will another person do it?"