My SAT super score: CR 690 
M 770 W 800
My ACT score: E 33 M 35 R 31 S 34
I will be apply for CS to engineering schools such as Georgia Tech, UIUC, UMich, Berkeley and a few ivies.
Should I report the ACT score? Or is the SAT higher/ sufficient?
Finally, will a retake of the ACT at a target of 34-35 be prudent to increase my chances? (International Student)
Be aware that UIUC, Berkeley and UMich do not superscore SATs but instead use that test with the highest composite and thus that may mean you should be seriously considering sending that ACT if you need superscoring to give you your mentioned SAT scores. Georgia Tech is one of the rare colleges that actually superscores the combination of ACT and SAT tests. It uses to determine admission the higher of the SAT or ACT math, plus the higher of the SAT CR or ACT English section, plus the higher of the SAT writing or the ACT combined English/writing score. It totally Ignores, even if you submit only ACT, the ACT reading and science scores. As a result, for it you should be considering sending all scores and you definitely should send the ACT.
Your ACT score is in range for any of the colleges you mention and there is not a need to retake. I cannot tell about your SAT because you provide only the superscore.
Thank you. My highest SAT sitting is 2250 with a 690 CR 760 M and 800 W.
How does that change the equation for Berkeley/ UIUC and Mich?
And yes, I will definitely send the ACT score to Georgia Tech.
You should likely just send all scoes. The test scores are close to each and for colleges other than Gtech,which superscores the combination of the tests, the colleges will use for admission that test, ACT or SAT, they believe is better for you if you submit both SAT and ACT. Also, submitting all scores avoids the essentially impossible task of trying to figure out the impact of the differences among what colleges consider. For example, you mention UIUC and in passing the ivies. Since you are interested in CS, I am assuming Penn may be one those ivies to which you intend to apply. UIUC does not use the writing section of either the SAT or ACT to determine admission, and beginning with the entry class of 2016, neither will Penn. Moreover, many colleges consider the math and English sections of the ACT to be the more important scores. In addition, the ACT/SAT score comparison tables you find online are guidelines not rules. The last ones were created by SAT and ACT in 2007 based on tests from 2005 and 2006, so what you find online is also dated. Colleges may have different comparison tables based on more recent data and based on data of their own applicants rather than the general population comparisons you find on line (both the College Board and ACT.org actually recommend that colleges create their own comparison tables if they intend to do comparisons). In other words when scores are within the same general range, you likely are better off submitting both tests.
Thank you for the detailed response. On a side note, I have taken the SAT Physics test today. Although I have ordered free score reports, I am not confident of scoring as well as my other 2 tests (M2 - 800, Chem - 800). So, if I end up with a 750, will the colleges above (esp. Penn/ Berkeley/ Cornell) hold it against me? Should I not report a physics result then? Or will my other two scores meet the requirement?
Cornell requires applicants to provide all subject test scores but it uses to determine admission the highest two. Penn and Berkeley recommend but do not require two subject tests and you can send to either whatever subject tests you want to send, so if you have a bad score out of three tests, consider not sending it. However, a 750, if that is what you get, is a good score and there would be no reason to withhold it.