Examples of these include their rRNA, and their RNA polymerase. Their way of carrying out transcription is actually most closely related to that of eukaryotic cells. Their DNA replication is similar to that of Eukaryotes too. In fact, most of the processes relating to information processing, while unique to Archaeal organisms, are related to those of Eukaryotes, and are completely unrelated to those of the bacteria. These tend to deal with processes relating to metabolism, uptake and motility for example.
Some Archaeal features are a unique mixture of both eukaryotic and bacterial processes.
It is interesting that the assimilation does not seem to go both ways. Researchers are currently studying C-1 metabolising archaea and bacteria, looking for evidence of gene transfer. There are interesting metabolically mutualistic relationships between the various C-1 metabolising organisms.