Another one: Would you upgrade your Cutty black to a Corsair if you already had a Cutty Red? The Corsair is basically an upgraded Cutty Black right?....
Por que no las dos?
For what it's worth I have a Cutlass Red and a Corsair, but I think there is a case to be made for keeping the Black instead of upgrading it.
(Eventually) You can slave the turret to pilot (or co-pilot) controls making it super easy to solo. Cutlass Black is a surprisingly solid combat ship even without 2 "gimbaled" size 3 cannons on the turret accessible. It's also fully functional with 2 players and has room for 3 (plus more in the drop seats in the back just in case) so it's very flexible. It has a generous cargo space and room for bikes and/or rovers.
Corsair ticks many of the same boxes as the Cutlass, that's for sure. They're both cool looking and have lots of flexibility. But the Corsair is going to handle worse than the Cutlass by a noticeable margin and is a much bigger target. Corsair has more room for more friends and cargo/loot, more firepower, longer range, and better sensors. Cutlass Black is also (less than) half the price of the Corsair.
I think they're both great looking ships. I fly my Black in the PU more than my Red because while the Red is great for it's role, not having any turret or any missiles sucks when you get jumped.