I don’t like either very much, but that being said, I’d generally recommend a good moving magnet cartridge over a cheap moving coil, for a variety of reasons.
If you have say around $500 to spend, and assuming you are chasing a medium compliance cartridge for a typical medium mass tonearm, there are lots of choices. Moving coil cartridges are technically better for a number of reasons, but at this low price point (yes, $500 is low priced for cartridges), moving coils are almost always high output types, of basic construction and generally don’t sound great. An exception is the venerable Denon DL-103, but it’s not suited to lower-mass arms.
Why? Cheap cartridges with aluminium cantilevers and spherical or elliptical styli don’t sound amazing, whatever the flavour. A nice moving magnet at this price probably has a better diamond, and better cantilever and is going to sound warmer, punchier and probably a little easier on the ear, even if it does lack resolution. There are no surprises here.
Much beyond $500, moving magnet cartridges don’t get a lot better because they are technically limited by the mass or inertia of the moving elements. Low-output moving coils start to come into their own at around the $750 mark. From here, the advantages of moving coils become critically important and this is why most cartridges I recommend from $750 are MC type. The equally legendary but better Audio Technica AT-OC9, in affordable XEN configuration is available at this price point and crushes most similarly priced MM carts.
This is why basically all high-end cartridges are coils. It’s also why all of my serious carts are and have been moving coils. listen to any good system and you’ll hear it, but it creates that age-old equipment problem of wanting to spend more and more money! Keep in mind though that you need an altogether better playback chain to get the most out of a low-output MC cart.
A classic rookie error involves listening to a good low-output MC cart on a phono preamp that isn’t good enough to extract the best out of these designs. You’ll never hear all that the low-output MC cart can do because of the limited resolution of the phono preamp. The best solution is a better preamp and/or high-quality step-up transformer.