How to choose a cartridge?

You can generalize a bit using various specs ( stylus profile, cantilever material, magnet type, coil materials, etc. ) however carts, being basically handmade transducers, are very much a product of the maker. I find it fascinating how different carts can sound despite using similar materials and techniques. 

For some this is the fun of it ( trying, learning )...

I don't have a experience with a extensive range of Cart's.

I have owned approx' 10 Cart's from MM, Ceramic, LOMC and HOMC, and am familiar with Three Cart's used regularly on my system, the main one in use being an Ortofon Rebuild, the lesser used ones being a low usage hours Ortofon Kontrapunkt b and a low usage hours Hana SL.  

I am not too impressed with the Hana SL, it does not present in a manner that captures my real interest, but it is a reasonable Cart' for the asking price.

I have been quite impressed by the reintroduction and use of a Audio Technica AT-150MLX, this might be a place where I end up in the not too distant future. 

I have heard the Len Gregory Moving Iron in the past when I was accumulating experiences of Cart's and was not too taken to this design in the system it was demonstrated in. I believe the Len Gregory has a Grado as the Donor Model.

In a demonstration carried out on a TT > Tonearm with a detachable headshell, a range of Ortofon Cart's and derivatives of the Ortofon Cart's were all mounted into the same headshell types and compared to each other.

The Cart's between them had a FGS, FG 80 and a Ogura Vital Stylus.

At the end of the demonstrations it was a shared thought between the attendees that the idea that the stylus only was responsible for the noticed differences would be an inaccurate assessment, it was agreed that the most likely influence was the overall assembly and used materials for the devices that were the responsible for producing the differences being detected.       

Dear @holmz : First than all you need to define in precise way which are your main targets for the reproduction room/system quality levels.

After that and your investigation and everything the same yes it's: 

" Does one just flip a coin? "

or if you are lucky enough after all those maybe 1-2 of the cartridge sources around your area could have one of the cartridge alternatives you want it.

I know that you like measurements as you mentioned, well with cartridges that almost does not works to make cartridge decisions.

Btw, of the ones you named the LPS has my vote.

Regards and enjoy the MUSIC NOT DISTORTIONS,

R.

When my Lyra Delos started to sound a little grotty, I replaced it.with a Hana ML. I used my Denneson Soundtractor alignment tool to mount it. It wasn't very much trouble as the Hana's body is nicely rectangular. I mounted it on my old but still willing Alphason arm. The Hana cartridges all want two grams stylus pressure, and it's an easy number to home in on. It sounded lovely from the very first time I dropped it onto a record groove, and it continued to improve over the ensuing couple weeks. I'm a happy guy. It sounds beautiful and it tracks at least as good as the Lyra did in its salad days.

It is very hard to even begin to recommend something absent some kind of context as to sonic preference and what you are trying to achieve.  It would help to know what cartridges you have heard in your own system or a system you know, and what kind of sound you are trying to achieve.  For example, if we know what you have for gear and what direction you want to move from your current sound, someone can probably point you in the right direction.  If you have heard cartridges that are sort of at the extremes, like a vdh Colibre (fast, clear) and one at the other extreme, like a Koetsu (warm, harmonically dense) and have a preference, that would be helpful too.