In what ways are the archaebacteria different than the eubacteria?

They are both very similar if you just look at them under a microscope. That's why we thought they were all just one big group until several years ago. You have to look at the subcellular level to see what make them tick. It was Carl Woese who found out they were different by comparing the 16S subunit of their ribosomes.

By the way we are more like archaea than bacteria. Creepy.

Archaea have more complex RNA polymerases than eubacteria, Archaea also have different membrane lipid bonding from eubacteria.