Both flood myths are certainly similar that it is sound to reason that they may have similar origins or one draws from the other. The Noahide flood myth is detailed in Genesis chapters 6 through 9 of the Jewish/Christian Bible. The Ziusudra flood myth is from a single tablet often called Eridu Genesis.

Similarities

Both floods are brought about by divine intervention.

Both floods were for the express purpose to destroy mankind.

Both persons build an ark to survive the flood.

Both persons save pairs of animals as well.

Differences

Ziusudra was a king; Genesis neither states nor implies that Noah is anything other than average.

Ziusudra is part of a mythology that involves a pantheon of gods; Noah exists within the monotheistic Jewish mythology.

Enlil, a god to Ziusudra, was annoyed by all the noise that human cities and activities made, so he persuaded the other gods to wipe out mankind. Noah's God was grieved that he had ever made mankind because every thought and action of their's was only wicked, so he decided to destroy them.

Enki, another god to Ziusudra, was fond of Ziusudra so he resolved to save him in some way. Noah's God seems to be conflicted, favoring Noah because he is actually not wicked, so God resolves to save Noah, his family, and the animals.

Ziusudra is rewarded by the gods with immortality. Within the myth itself, Noah is not rewarded with anything (some theologies certainly say he has eternal life, but that is not derived from the myth itself). In fact, Noah praises God and sacrifices and worships!

Ziusudra's gods don't seem bothered that so many were killed. Noah's God promises that he will never again destroy mankind, showing perhaps regret for the whole affair.

Ziusudra's flood myth doesn't seem to bother with rebuilding and re-population; there's no pragmatism, as is typical for myths. Noah's flood myth goes into this a great deal (i.e. there's genealogies, locations named, who settled where, etc.) and the stories in Genesis start to sound a little more plausible and less like epic legends.

Conclusions

The dating of each myth suggests that the Sumerian Flood Epic (2300 BCE) may very well have influenced the development of the Jewish Flood Epic (1400 BCE to 700 BCE depending on who you ask). Many scholars believe that the whole Genesis creation myth (the first 11 chapters of Genesis) was influenced by the Babylonian version of the epic of Gilgamesh, which does mention a flood. Further, the Jewish people were held captive by the Babylonians in the 7th century BCE. This surely influenced their culture and already existing myths.

Jewish culture stands out among most other ancient cultures. Generally, they were xenophobic and extremely resistant to syncretism. They would fall away and worship other gods, but they were always defined by their "one true God". You can see this in the Noahide adaptation of "the flood that wiped out mankind". In Ziusudra's myth, the gods look at man like a plaything that entertains and aggravates them. The Jewish god loves his creation dearly and is grieved when they do wrong, not annoyed. Ziusudra's gods are one dimensional, having particular characteristics and persuasions, while the Jewish god is multifaceted and sometimes seems to contradict himself as a consequence of adapting these epics to revolve around a monotheism. In light of this, the differences between the two myths makes sense, while the core similarities remain.

Sources