The major structure that plant and animal cells have that a bacterial cell does not is a nucleus.

Here's why:

* Eukaryotic Cells (Plant and Animal): These cells have a true nucleus, a membrane-bound organelle that contains their genetic material (DNA). The nucleus is responsible for regulating the cell's activities.

* Prokaryotic Cells (Bacteria): These cells lack a membrane-bound nucleus. Their DNA is located in a region called the nucleoid, but it's not enclosed within a membrane.

This difference is a fundamental distinction between these cell types.