How are my taxes impacted if I work in New York City and live in Connecticut? Will I incur income taxes for both states? At the end of the day, will I be paying more taxes vs. living & working in Connecticut?

If you work while present in NY city, you must file the state return and report income while in the state. You will file return as nonresident.
Then in Connecticut, you will file as resident and report your world wide income including income when you worked in NY city. You will also claim credit for the taxes paid to other state.
Read: Your U.S. Tax Return: Working in two or more states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)

At the end of the day, will I be paying more taxes vs. living & working in Connecticut?

Yes, you will most likely pay more taxes working in NY than living and working in CT. Reason is that tax rates in NY are typically higher than in CT (6.85% max rate in NY, versus 5% in CT).