The best criteria for classifying cells as either eukaryotes or prokaryotes is the presence or absence of a true nucleus.

Here's why:

* Eukaryotes have a true nucleus, a membrane-bound organelle that contains their genetic material (DNA).

* Prokaryotes lack a true nucleus. Their DNA is located in a region called the nucleoid, which is not enclosed by a membrane.

This fundamental difference in cellular organization is the defining characteristic that distinguishes these two major domains of life.

While other criteria can be used to further differentiate eukaryotes and prokaryotes (like the presence of other membrane-bound organelles, size, or ribosome structure), the presence or absence of a true nucleus remains the primary defining characteristic.