Using would rather/sooner

Would rather and would sooner have the same meaning as would prefer. However, the grammar is slightly different.

I'd prefer to be rich than poor.
would prefer + to + verb (infinitive with to)

I'd rather be rich than poor.
would rather + verb (infinitive)

I'd sooner be rich than poor.
would sooner + verb (infinitive)

If we talk about things we want another person to do, then we use a past form after would rather/sooner.

I'd rather you were rich than poor.
would rather + subject + past simple

With prefer there is no change in tense.

I'd prefer you to be rich than poor.
would prefer + subject + to + verb