Well, you have already started to figure out where to start, and as a SOTA owner myself, I would stick with that. As you say, your friend has the same, and his rig sounds better. So….
I believe your arm is basically a Jelco, perhaps a 750, rebranded by Sumiko. That isn’t a bad arm, at least I doubt it is the weakest point. Which points to your cartridge, and/or phono preamp, as the two pieces I would start to look at upgrading first. Or, the cart and arm, if you like your phono pre.
No doubt his Triplaner is a better arm, but so is his cartridge, and that is personally where I would start. The 103 seems to have a great following, but it isn’t a Lyra. That was a $5,000 cart (still sell in 1.5-3k range used today). Carts do make a significant difference, it’s up to you to figure out how much you want to spend to get the same/similar sound. I would start with the cart first, then, a toss-up between the arm and preamp, but I think a preamp could make a more immediate impact.
