while the cartridge does need to be compatable with the arm's compliance in a general sense, most cartridges are compatable with most arms these days. and if a cartridge or phono stage is too colored to match the other, then one or both are to be avoided. if you have an extremely low output MC (say below .2mv) then obviously it is essential than the phono stage be high gain low noise. these are all common sense issues, but to comment one must first state the obvious.
so assuming all those things, the most important issue (setting aside spot on setup) is the arm; a great arm will make a moderatly priced but well chosen cartridge sound refined and musical. a mediocre arm holds back the best of cartridges. i'll take a top level arm with a moderately priced cartridge every time over an expensive cartridge and a mediocre arm. an arm is the 'hard part', it does the heavy lifting in a vinyl set-up. it allows the cartridge to attain that precise set-up and groove tracking ability where the magic happens.
i've compared arms and compared cartridges, and when the arms are different things are much more different than when the cartridges (within similar price ranges) are different. arms are even more significant than tt's with similar designs. you want to upgrade the performance of your vinyl, get a better arm.
better arms have the potential to have less distortion. period.
so it's not so much a matter of cartridge-arm interface verses cartridge-phono stage interface as much as it's simply getting the very best possible arm you can, making sure it is solidly attached to the plinth, and then setting it up perfectly.
i've had more than a few cartridges, more than a few tt's, more than a few phono stages, and more than a few arms. in the last couple of years i've been fortunate to watch development of a series of tonearms, and it is easy to see where the real performance in a vinyl setup comes from.
as arm performance improves, cartridges get better and better, and previously held perspectives on cause and effect get hit with the real truth. once you reach a certain level of cartridge quality it becomes a flavor issue, once you reach a certain level of phono stage you pay astonishingly higher dollars for dramatically diminished returns.
arm performance is like bass performance in a system, until you hear bass in your system without the distortion, you won't realize that you have been listening to distortion, it's an experiential thing. you cannot explain it to someone, they have to hear it for themselves. their reference for bass performance must change.
arms are like that too.
so what does that matter in terms of cartridge choosing?
the least colored cartridge will continue to improve as the arm improves. as you remove distortion from the arm, the true character of the cartridge will be more and more evidant. likely you are moving down a system path desiring better, lower distortion, sound.
12 years ago i had a Koetsu RSP as my reference in a Levinson-Wilson system. it balanced. since then i moved toward lower distortion, more natural sounding systems and even though the RSP still had a piece of my heart, it was exposed as being too colored to live with. i sold it a couple of years ago.