Which theory could be used in comparison with the Orientalist theory?
Since Said’s Orientalism is broken down into three historical phases, I would use New Historicism as a comparison with this theory. You could also use post-colonialism as some of these issues would overlap. But, you could go with New Historicism (let’s say you’re working on Iranian literature) to look at the representations of Middle East Muslims in Western (English, American, French, etc.) Literature. Then, of course, look at representations of Middle East Muslims in Middle Eastern Literature. Said’s theory was that literary theorists and writers of the West perpetuated stereotypes of the East as inferior. Said seeks to decode these representations and challenge those who perpetuate them. Since Said is talking specifically about Muslims, you might want to use Said’s theory as a background and go with two New Historical Approaches: one from the West (American, British, or even Israeli) and one from the East (Iran, Jordan, Palestine). New Historicists attempt to be neutral in their diagnosis of history by objectively analyzing literary and non-literary texts. So, this means being aware of your own (critic’s) potential biases as well as the biases of the texts and writers. Easier said than done.
You could also use Marxism, post-colonialism, cultural materialism. New Historicism is the most obvious answer, but one of these might fit your project better. It’s hard to say unless you specify how and to what you’re applying Orientalism.