I am in the same boat. My son has a 2011 iMac and running into FPS issues with Minecraft with MODS that he plays all the time. I don't really want to build a PC, as my older son had to wait til he moved out before I would help him build one, but looking at FPS on M1 versus a built PC is maybe 50FPS with MODS on M1, versus 300 FPS on a built PC. How does Minecraft run with MODS on the M1 Mac Mini? Thanks for the help.
I play a lot of minecraft on my M1 mini, Before, until 1.18 I used ManyMC as the launcher, since Oficial launcher was not native. it ran at 40-55fps on my redstone nightmare word (read as LAG AF) tried to install optifine mod for better FPS but had no sucess, optifine tends to increase FPS by a lot, and is basically necessary for minecraft java, I use it even on my windows with a 980Ti. Now on 1.19 it runs natively on oficial client, but last time I played there was no optfine mod available yet and forge (required to run it) didn't run at all, but if everything works, expect it to run at 60-75FPS in general or being optmistic maybe it can go all the way to 80-90.
Also You need to check which types of mods are running, are they for props, mobs, and itens? those generally don't impact FPS too much, but shadders will sink the FPS even on decent windows machine since it uses a lot of GPU power, the Mac Mini M1 has the equivalent power of a GTX1050, which is more powerfull than a 2011 iMac but basically a entry level graphics card, and since it shares video memory with ram on the M1, It's not very advisable to try running shadders on a 8gb mini, and still, FPS will suffer, A LOT.
If you really want a absurd ammount of FPS specially on old hardware, The ideal is not even going to optfine but sodium instead, it basically makes the game go from 10fps to 100+FPS, but.... it requires Fabric instead of forge, and not many popular mods are made with Fabric in mind. still a amazing way to get decent FPS on agging machines.