The characteristic that is not shared by eukaryotic and prokaryotic cells is the presence of a nucleus.

Here's why:

* Eukaryotic cells have a true nucleus, which contains their DNA. This nucleus is enclosed by a membrane.

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

Let me know if you'd like more information about other differences between eukaryotic and prokaryotic cells!