Is that smart to compare my method with that proposed by my external examiner? Of course, his/her method won't produce results as good as mine. So I wonder if it will minor my chance to pass my viva?

Many thanks.

If you and your external have comparable methods relevant to your thesis then it needs to be acknowledged and debated. This is assuming your external has published this method, unpublished conversations do not count! Rather than suggest they won't produce results as good as your methods, it would be wise to be constructive as to why your methods may be better but also noting any weaknesses in your methods too. It may make for a lively debate but you shouldn't be failed for it. If the external has relevant publications related to your work that are not included in your thesis could cause you more problems.