She did what I desired. = She did that which I desired.

[vil]

Dear teachers,

Would you be kind enough to tell me whether the following two sentences are enjoying the same rights?

She did what I desired.
She did that which I desired.

Thank you for your efforts.

Regards,

V.

[konungursvia]

Yes and no. The former is less archaic, the latter very so.

Even "desired" is rather dated compared to "what" as a conjunction.

Natural English in our times would prefer: "She did what I wanted."

Or, more formally, "She did as I desired."