What is the difference between 偉大 and 偉い ?Feel free to just provide example sentences.

偉大 is great, grand,distinguished meaning.
偉い is great, superior, distinguished meaning.

Almost same, but in my feeling, 偉大 is stronger than 偉い.

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In detail

The usage is a little different.

If you describe something using "偉大", it needs conjunction "な".
When the end of sentence, it needs "です" or "だ".
for example: 偉大な人( great person ),　彼は偉大です。 ,"彼は偉大だ。"

偉い don't need conjunction "な".
for example: 偉い人(great person) .
偉い meaning for person is about position or status, or one has done.

And 偉い, we don't use "だ" on the end. ( we don't say "偉いだ"）
We use "です". (偉いです)

If you add noun after "偉い", you can use "だ".
for example: "彼は偉い人だ。(he is a great person)"
We can also say "彼は偉い人です".

I think it is difference.