What is the process when the admissions office receives 2 ACT scores (superscore) and 2 SAT scores (superscore)? Which ones do they choose?
Depends on the school’s policy, but most likely they use the official SAT-ACT concordance and select the higher (if they superscore at all).
If they don’t superscore, they’ll use the concordance to find the highest single sitting.
I don’t think I’ve seen any schools that superscore between tests, though some may exist.
my guess is that some admissions officers will be annoyed by getting both. I don’t see any reason to do it and you might look like a suck-up.
You can definitely send both ACT and SAT scores, if they are strong scores.
Unless a college specifically asks for “all” scores to be sent, you will only need to send your best score from College board
If you send both ACT and SAT, colleges generally use that test, SAT or ACT, which they believe is the higher in determining admission, and if they superscore both the tests, they will use the one with the higher superscore. When your SAT and ACT scores are close to each other based on the ACT/SAT conversion charts you find at the ACT or College Board sites, it may be better to send both because the college itself may follow a somewhat modified conversion chart and thus you cannot be certain one score is really higher than another just based on those publicly available conversion charts.
Moreover, there are colleges, UIUC is one, that use that test with highest composite to determine admission, do not superscore, but its colleges may consider another section score from a different test, e.g., its engineering department uses the test with highest composite, officially does not superscore, but if the other test (ACT or SAT) has a better math score, it will consider that in determining admission.