They both lack a nucleus and contain cytoplasm.
The unique functional adaptations of Archaea are more similar to Eukarya adaptations.
They both evolved in the same geological time period.
Genetically, the Archaea are more similar to Eukarya than Bacteria. 
They both have membrane-bound organelles.
Archaea is not closer to Eukarya because it contains prokaryotic cells just like Bacteria.

Archaea are unicellular prokaryotic organisms, which share many characteristics with bacteria, however, the existence of metabolic functions and genes similar to eukaryotic organisms suggest that there is a genetic link between the two. Even the enzymes responsible for genetic processing, such as transcriptases and translation enzymes, are similar to those in eukaryotic cells.

The theory that establishes the relationship between Archaea and Eukaryotic suggests the existence of a common ancestor, whose later evolution allowed an Archaea to join a protobacteria to form a eukaryotic cell, and hence their genetic relationship.

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