Gain RequirementsThis side of the comparison is 100% in favour of the High Output devices rather than the low output ones. (Yes there are such things as Low Output MM's as well!)
Basically the more gain (boosting of the output) is required in the system (ie the lower the output of the cartridge) - the more difficult it is to make the phono stage (or phono stage and step up transformers) sound good.
Higher gain all else being equal, also involves higher noise and higher distortion.
So to achieve equal levels of quality in the output of the phono stage, it must be substantially higher quality.
The lower the output of the cartridge, the higher the quality of the phono stage required to amplify it for the same equal quality result.
To put it simply a $300 phono stage that only has 40db gain (used for HOMM and HOMC) will sound better than a $300 phono stage that has 65db gain.
For similar quality in the higher gain stage, you need to double the cost (roughly). - Of course if you double the cost of the lower gain stage there are improvements to be made there too...
If you include the additional cost of the phono stage (and/or transformers) then a strong argument can be made that the two types are very much equivalent in quality. (ie $300 phono stage with $700 HOMC cartridge, vs $600 phono stage with $400 LOMC cartridge....)
High vs Low Output - number of turns of the coilsTo put it simply, a high output MC achieves its higher output by having more turns of wire in the coil - more turns = more voltage...
So to achieve its higher output the HOMC has to have more wire attached to the cantilever, more mass on the cantilever is a negative - it increases the inertia of the cantilever.
For high performance, and the ability to properly track high frequencies (which require that the needle change direction many of 000's of times per second!) - the equivalent tip mass of the stylus needs to be below 0.3mg.
Most HOMC's have trouble reaching this low mass (and therefore their tracking ability at higher frequencies is reduced) - example: Early version Ortofon X5-MC (HOMC) had effective tip mass of 0.4mg, current production is using lower quality cantilevers and is specified at 0.75g effective tip mass.
At the same price point, Ortofon's Rondo Red (LOMC) has an effective tip mass of 0.3mg
Both designs use an aluminium cantilever, assuming you had the earlier higher quality X5MC, the additional turns of wire are adding approximately 0.1mg of additional mass to the stylus tip.
On the other hand, if that were a boron rather than aluminium cantilever - lets look at another example:
Ortofon MC Jubilee with a VERY fine boron cantilever achieves 0.22mg stylus tip mass - if one was to fit the additional turns of coil wire required to provide this as a HOMC design - it would add around 0.1mg making it 0.32mg....
That would provide pretty much the level require for very good HF tracking - while also providing the advantages of high output.
So: It is POSSIBLE to create a HOMC with similar levels of tracking ability (due to low stylus mass) to everything but the best TOTL LOMC's. (Ortofon's lower end LOMC's often have stylus tip mass of over 0.4mg eg: MC Salsa, Samba, MC25, )
Most manufacturers do not quote stylus tip mass... so you are left guessing...
A cartridge with a boron or a ruby/sapphire cantilever is usually an indication of very low tip mass. All else being equal the HOMC will have higher stylus tip mass.
NOTE: it is often forgotten that the lowest tip masses achieved have always been on Moving Magnet designs and not Moving Coils. Fundamentally, a high efficiency small magnet is lighter than even minimal coils. - And on MM designs that accept lower output (similar output to many HOMC's - around 1.5mV) the stylus tip mass is in most cases lower than the equivalent MC. (even though the mythology says the MC's are lighter! - check out the specs for cartridges like the Technics EPC100mk4 - less than 0.1mg, or EPC205mk4 less than 0.15mg)
Permeable vs Non-Permeable coresHigh output MC's and most low output MC's as well use permeable coil formers.
These have the advantage that they are more efficient - and therefore provide a higher voltage output... the downside is that they have a whole series of distortions that are in common with all magnetic cartridge designs other than MC's with non-permeable coil formers.
Cartridges with non-permeable coil formers have low voltage output (sometimes VERY low voltage output)... examples of this rare breed of cartridges includes:
Denon DL304, DLS1, Fidelity Research FR-7, JVC L-1000, Benz-Micro Ruby, and most Lyra models.
NOTE: almost all step-up transformers suffer from the same type of distortions - this is one of the advantages of a solid state MC phono stage...
My PreferenceI don't have one. (a favourite)
Whether running HOMM or LOMM or HOMC or LOMC - the best cartridges out there are totally competitive with each other. (some categories are not currently being made and are therefore rare as hens teeth - eg: LOMM)
For best results make sure you look at the system wholistically - the cartridge needs to be a good match for the arm, table, and phono stage. (including things like cartridge loading, damping, compliance etc...).
I have a theoretical leaning towards LOMC's with non-permeable cores... but I have several HOMC's and LOMC's.... (and none with non permeable cores!)
The Dynavector Karat (LOMC) with its tiny 2mm cantilever made of Ruby is quite the "gem" - primarily caused by exceptionlly low tip mass, and cantilever rigidity....
I very much like my Pickering XLZ7500s LOMM - which requires the same level of gain as a LOMC... Not sure why it sounds so good! Tip mass is unknown - I don't believe it is in the super low tip mass category - although it certainly is in the low tip mass class.
I am currently seeking a needle for my Technics EPCP205mk3 - it has an exceptional magnetic system (the equivalent of the MC non-permeable cores?) - but have not been able to find a stylus for it

Hope this helps,
bye for now
David