Like the turntables question, there’s a bit to this one but simply put, the very best cartridges are moving coil.
That isn’t to say there aren’t some fantastic moving magnet cartridges out there, especially some of the vintage ones. Rather, the best solution, technically speaking, is the moving coil design, mostly because of its reduced moving mass and therefore better transient and high-frequency performance. A really good magnet will be better than a cheap coil though. You always get what you pay for.