Stability
DNA (deoxyribonucleic acid) is double stranded hence it is stable. RNA (ribonucleic acid) is single stranded, hence it is relatively unstable.
Mutation
Mutation is the change in the sequence of nucleotides which comprise the genetic information. Mutations occur in macromolecules which are relatively unstable. RNA is unstable and therefore mutates faster.
Hence, the pathogenic virus with RNA as the genetic material mutates faster as compared to the one having DNA.