Both expressions are correct. I believe the first one is more common for such an expression. The second one is more preferably used in a topic sentence where the first part (ミサの目) is followed by (は), and then you can express multiple states about the eye like (Misa has big brown eyes) can be expressed as --> ミサさんの目は大きくて茶色いです。Or ミサさんは大きな茶色の目をしている。

I think "ミサは目が茶色いです。" is more common. ミサの目は茶色です。 ミサは茶色い目をしている are better I think. 「は」represents a main topic. In this sentence, main topic is "ミサの目". So I choose "ミサの目は茶色です"

For your information, Japanese people almost always refer "brown eyes" as 黒い目 when we talk about the color of the eyes. When Japanese people say "brown eyes" Japanese people think that the speaker is talking about a person with light brown eyes.