My ACT score recently came out, which is a composite score of 34 (35 English, 36 Math, 35 Reading, 31 Science). I'm wondering whether compared to my SAT score 2220 superscored (740 Math, 800 Writing, 680 Reading), I should send the...

... ACT or SAT score? I know that the 34 and 2200 composite scores do not differ much, but my math and reading on the ACT are better than my SAT ones. Or should I send both exams to colleges?

According to this site a composite ACT score of 35 is equivalent to an old SAT score of 2340 so you are correct that your ACT score is stronger than your SAT score.
http://www.testprepcoach.com/convert-act-score.html

I would suggest that you should ONLY send your strongest test scores - in this case your ACT score. As an applicant you want to present your strongest academic results to colleges so unless you are required to send in all your testing scores you should only present your strongest scores.