What are some important characters in Shakespeare's plays and how were these characters different from similar characters in other Elizabethan plays?

I'm guessing it wouldn't help you to list important characters in Shakespeare's plays as many of the tragedies state their important characters in their titles (Romeo and Juliet, Othello, Hamlet, Macbeth, King Lear, Timon of Athens, Coriolanus... and so on) and many of the comedies have dramatis personae with several important characters (I'd argue, for example, that Twelfth Night has no 'lead' character: but that Viola, Malvolio, Olivia, Feste and Sir Toby all occupy central positions).

But if, as your second question suggests, you want to compare characters from Shakespeare's plays to characters from other Elizabethan works, then I can offer you some good points of comparison.

Shakespeare's Shylock (The Merchant of Venice) against Marlowe's Barabas (The Jew of Malta) - a far more worked out version of the 'evil Jew' literary stereotype that was dominant at the time.

Shakespeare's Coriolanus (Coriolanus) against Marlowe's Tamburlaine (Tamburlaine the Great) or Jonson's Sejanus (Sejanus) - Coriolanus is undoubtedly a more psychologically complex figure than either of the others.

Shakespeare's King Lear against King Cambises: a comparison which hardly bears making, but will show you how much more humanity and detail Shakespeare invested into his characters than earlier dramatists had done.