So here's a quick look at the bottles:



You can see that Tudor City Teal is the slightest bit more richer or saturated than Turquoise and Caicos. Tudor City Teal looks a little more blue and Turquoise and Caicos is a bit more green. I would say that they are still both the same amount of dusty, though.
I will say this off the bat but I hate the formula for Essie Turquoise and Caicos. It's so awful. It's patchy and uneven and really thin for what it's supposed to be. Tudor City Teal on the other hand applies very nicely and smooth. Here's a check-in at one coat:



At two coats, Tudor City Teal is pretty much good to go whereas Turquoise and Caicos could use another coat. Here's two coats with no top coat:



Overall I think they're similar enough to not require having both of them in your collection. If I had to pick one, I would definitely go with New York Color Tudor City Teal because not only is it far cheaper in price, but the formula is just so much better.
What do you think of these two? Do you think they're similar enough? Is there one you prefer over the other?