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Both are important.
A cartridge has a compliance rating and must be matched to a tonearm that has an effective mass that can properly handle this rating.
A cartridge must also be used with a proper phono stage - MM or HOMC with a MM preamp and LOMC with either a MC phono preamp or SUT.
It’s trickier to get the first one right because the tonearms effective mass is not always known. Its easier to do the latter. But both must be properly matched to get the best sound from your rig.
The former, for sure. The problem is that most people are focused on the primary resonance of the cartridge/tonearm system. If too far off the primary resonance can either be excited by record warps on the one end and the lowest tones of the music on the other. However most modern cartridges are of medium compliance and most modern arms of medium mass, minimizing these problems. Although this is a tracking issue, the problems don’t fall within the audio range.
On the other hand, what does fall well within the audio range are the secondary arm/cartridge resonances. These have a much greater effect on the sound that you hear. Then why all of this focus on primary resonance? Because it is easy to calculate and to measure. Secondary resonances are quite hard to measure. It’s a case of measuring the less important thing.
Which brings us to the uncomfortable truth that, unless there is a gross mismatch in the primary resonance, the only way to know what cartridges work well is which arms is by anecdotal evidence or trial and error.
First cartridge/arm match, then with phono. Can we also match cartridge to the table itself? Well, when considering an inexpensive cartridge for my Nottingham Spacedeck/Spacearm I tried to factor this in too. The Nottingham designer himself thought that his tables are on the warm side and a little dark. So considering everything I came up with $375 ( from the UK ) Goldring 1042 MM. I already had Acoustech phono that I knew would handle any of my choices well. My future upgrade for this set-up could be Lyra Delos, but that's $1600 ( again from the UK ).