What is the preferred cartrige mm or mc and why


Curious to know why some audiophiles prefer a moving coil cartridge over moving magnet type. What determines this preference? Does the tonearm determine which type is preferred? Why? 
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I have 2 Shure V15 RS with a variety of Styli including a SAS. I also have an AT 14Sa. I have 3 MCs, a Denon DL-301 II, a very low mileage Dynavector 10x3, and a new Hana SL. Nothing very extravagant. The Shure is as close to perfect on a Linn LXV through a Nakamichi Receiver 2 as I'll ever get.

However on my Alexandria with a Sumiko MMT through a Musical Surroundings Phonomena II, I like the MCs better. I've been tempted to try a Grace F-9; but I fear that the supply of good styli will dry up. I don't see the wisdom of MIs without replaceable styli. What would be some good options in current production that would perform as good or better than the F-9? My MMT can only handle 4 - 8 grams.
2channel8, In this day and age, there is almost no such thing as a non-replaceable stylus.  Such companies as SoundSmith, Expert Stylus, at least two others in the US and one other in Europe, can replace styli on any type cartridge you care to name.  (Well, there may be a few exceptions.)  In some cases, a totally worn out or damaged suspension cannot be repaired, but otherwise, fear of stylus wear is not a reason to avoid this or that vintage cartridge.  I have had the stylus/cantilever of my Grace Ruby replaced by SS with one of their OCL styli on a ruby/sapphire cantilever, a la the original, and the sound is improved.  (I can say this because I also have an original unrestored Grace Ruby with its original elliptical stylus, and I have auditioned them side by side.)  Similarly, I own an Ortofon MC2000 that was repaired in Europe before I bought it.  I am also sure that SS can work on any MI type cartridge; they manufacture and sell excellent new MI cartridges.

The only issue that could arise, if you are a stickler for originality, is where the original stylus has a very exotic shape that is no longer available.  This might be the case for certain Ortofons, Stantons, and some others.  Actually Expert Stylus in England has some of these styli available.  Otherwise, you'd have to "make do" with a modern equivalent.

My experience with Shure V15s dates back several decades, but I found them to be totally underwhelming back then.  I would have guessed that the Hana SL might be your favorite among the MCs you named. By all means, do buy a used F9 or Ruby and have Peter L at SS replace the stylus; you'll be happy, and the Shure will gather dust.
As usual, @lewm , you make a good point. The cost of a ATN150MLX or Goldring D42 are not much less than Peter's services. But the Garrott Brothers P77i is only $270.

All-in-all the F-9 may be the better deal.
I use both MM and MC, like each cartridge - each has strengths and weaknesses. What I have noticed is that of the 3 phono preamps I use, the MC output is quiter - particulary on my new Parasound JC3 Jr - set to MM, it has an audible hiss when close to the speakers, not the case when I use it for my MC cart. YMMV

EDIT: 2 of the preamps I use have XLR output - same experience with XLR and single ended.