It's always better to take a taxi from JFK--if it's feasible and assuming you take a real taxi and don't get scammed by the dudes who try to hustle you when you're walking out of the airport with luggage.
As mentioned, they have pretty much set rates to go into Manhattan, and it's cheaper to go to other areas as well. I used to live in Williamsburg until very recently, and had to take Ubers from JFK occasionally when I landed at a terminal that had a bad taxi situation. The Ubers were expensive AF; over $100 total. Taxis were always sub-100, even when I used to live in Manhattan.
My main issue with taking Ubers from the airport, though, is that waiting for them takes forever and the designation pickup locations are clusterfucks. In contrast, the taxi stands have orderly lines. This is heavily terminal dependent, though; when landing at the American Airlines terminal, the taxi situation is great. The line is never too long and moves quickly. But, as mentioned, sometimes one lands at a terminal with a massive taxi line that moves like a snail. At that point, maybe one opts for an Uber--for which the wait is 10+ minutes, and may increase as time goes on and drivers are switched (!!), and the cost is extortionate.
In non-airport situations in NYC, taxis are always cheaper. Not always feasible outside of Manhattan (there aren't enough driving around in most parts of the other boroughs), but for any intra-Manhattan trip, taxis should be preferred.