Which of the two sentences should I use?
A: I haven't noticed that.
B: I didn't notice that.
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It depends on what you want to say.
I haven't noticed that.
In this context, you are using the present perfect tense to say it that a fact or matter has not been noted by you. Example: "I have not noticed the color of his eyes." You are not giving a specific time reference for when in the past that the not noticing happened. When using the present perfect in this way, you can't give a time reference. For example, you can't say, "I have walked last Tuesday." The way your sentence is formulated demonstrates the use of the present perfect in communicating a personal experience. Please see Topic 1 on this page: https://www.englishpage.com/verbpage/presentperfect.html for an explanation.
The present perfect can also be used to mean that an action took place in the past and continues in the present. "I have not walked my dog since last Tuesday."
Please see this page for a detailed explanation: https://www.grammarly.com/blog/present-perfect-tense/
I didn't notice that.
Here you would be using the simple past tense. You are stating that the fact or matter has not been noted by you in the past. You are not making any statement about how long your action continued. You are just stating that it happened. Example: "I didn't notice the color of his eyes. (But maybe that fact has changed; it could be that now you do.)