You're right; "maunawaan" is more formal than "maintindihan." In most contexts, they both mean the same thing, BUT in a more traditional sense, "unawa" has a deeper, more personal connotation than its Spanish-originated counterpart "intindi." Intindi refers to comprehending sentences and instruction, or reading between the lines; Unawa, on the other hand, not only means the same as "intindi," but also a profound understanding of a concept, sort of like having a higher level of consciousness... if that makes sense. >.>
With that said, you'd mostly hear the use of "unawa" in terms of reading the Bible or other deep literary material, because you're instructed to read between the lines and digest the meanings. You could also see the subtle differences when you use "unawain" and "intindihin" in terms of other people. They could have different nuances depending on the context.
Examples:
A: Nabasa't naintindihan ko na po ang sinulat niyo, pero—
B: Naintindihan mo nga, pero naunawaan mo ba?
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C: Hindi ko talaga maintindihan si Mama. Lagi na lang galit.
D: Unawain mo na lang ang nanay mo. Matanda na 'yan.
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E: Unawain mo na lang sila kahit nagkulang man sila sa'yo. Intindihin mo na lang ang sarili mo. (In this case, "intindi" means to look after yourself.)
Nowadays, the terms are interchangeable (save for example E), so you don't really have to choose which one fits better in a sentence, especially in casual conversation. But I thought you might like to know this bit of information. Hope that helps! :)