It would be a hassle, and a fair bit of work, but it appears that you are in a good position to compare these two fine tonearms, should you be inclined? Same cartridge set up on each, then the other cartridge set up on each? Just a thought.
I've not directly compared them. Years ago I decided to use a second arm for mono and a cheaper MM for less good quality records and some casual listening. I had a nice/OK Goldring, but now for a very good MI cartridge (Soundsmith/OL) running into the Luxman 509X internal MM phono amp.
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That cartridge did not fit on the Groovemaster headshell, so I put a Denon DL103R (Expert Stylus upgraded) on it and got a Phasemation headsell for the Soundsmith/OL.
For the Reed 3P I have a Koetsu Urushi rebuilt by Dominic Harper (NWA) with a Fitz Gyger cantilever/tip, I have a DV XX2Mk2 as a spare. I'll be in Japan in a month, may pick up an Ikeda 9TT.
The Groovemaster III with the Soundsmith/OL cartridge performs really well and it's beautifully made. It doesn't have that last bit of fine detail as the NWA rebuild, but I could listen to it all day. It comes in a load of options and lengths, which is useful, I have a 240mm version. There is a new Groovemaster IV, which ends up almost double the price.
The Luxman MC phono is nowhere near as good as the RCM. There's a Vertere Phono Mk2 L on the used market that I may get for it. I had the Vertere Phono Mk1 and it's a brilliant little thing, incredible value.
p.s. Just been doing some direct comparisons with Jeff Beck "Blow by Blow". I think the Luxman MM phono is letting things down a bit for serious listening. The 301 with the Koetsu on the 3P through RCM phono is really a bit mind-blowing. I think I'll buy the Vertere. It's a no-brainer. I had the Mk1 for a couple of years and made a profit on it, so nothing to lose.