Standard caveats:
Carrack: $500
Cutlass Red: $135 ($120 new money)
Avenger Titan: $50
The Cutlass Red does not have its medical gameplay beyond acting as a respawn point. Does not have its ship-to-ship docking functionality.
The Carrack is an exploration ship in a game with one star system
You
can heal yourself at the medical beds on the Cutty red since the medical function was an added feature with it's release, not only for the Cutty red but all ships that have a medbay (Carrack and 890J at present)... I tested it when the Cutty red was in PTU...hence why I CCU'd a Hull B for one... as well as having a mobile spawn point if you die, like in a mine or suchlike... which can come in handy, I actually like it...I was a big fan of the Cutty black anyway so the Red was a decent addition...only costing $5 to upgrade from the Hull B. It still has 16 SCU of cargo space in a separate sealed cargo area at the rear of the med bay so it can be used as a decent box delivery/minor cargo runabout as well as a medical ship.
You could always use the Carrack as a trader in the meantime, which is my plan...it has comfier seats than the Cat, an Ursa rover and the Pisces snub plus 456 SCU of cargo space, nothing beats that currently in game except the mighty Cat's 576 SCU so far.
Still better off going for the Cat if you're trader/hauler inclined in any case, it's far cheaper than a Carrack... Ship to ship as an entire mechanic doesn't exist...so it's not just an issue for the Cutty red...Most of the medium to large ships have the facility, it's just yet another thing Ci¬G have dropped again from the entirely functionless 'roadmap'.