Both are important. Missing on either will degrade the final sound.
The cart/arm interface is mostly concerned with the mechanical operation of the arm/cart/table. Things like alignment, mass, bearing design, etc., are the parameters here. We can make educated guesses using the resonance calculations here to see if a particular combo won't be grossly mis-matched but in the end we usually have to listen to a particular set to decide if they work well or not for us while playing music. Or, rely on the experience of others.
The cart/phono interface is mostly concerned with the electrical operation. Gain, internal resistance, tonearm cable, loading, slew rates, etc., are some of the parameters here. Here it gets more difficult as most times what works on company A's phono stage won't necessarily work the same on company B's phono stage, for instance. Many times issues in this interface can sound like mis-tracking when in fact we are hearing distortions. This, to me, really does rely on listening to get right, and many times input by the phono stage designer can be invaluable. Or, again, rely on the experience of others.
There is a lot more that can be said, but I hope this gets the basic idea across.
