What evidence suggests archaea are more closely related to a eukaryotic than bacteria are

- They have similar mechanisms for building RNA and replication of DNA 
- They use similar enzymes for building of RNA (RNA polymerase) 
- They have proteins which are bound to their genetic material (eubacteria do not have this). 

These are the main similarities. If you were looking at the differences of the eubacteria opposed to the archaebacteria and eukaroyotes, it would be that they have a different internal flagella structure, no proteins bound to their genetic material, different cell membrane structure etc.