The verdict

CPU
Bosgame M4 has 1.2x the CPU throughput (28,555 vs 24,021 PassMark).
Plex
Beelink GTR6 transcodes more 4K HDR streams (~5 vs ~3).
Idle power
Beelink GTR6 idles lower (12W vs 13W) - cheaper to run 24/7.
Networking
Bosgame M4 has more NICs (2 vs 1) - better for a firewall or VLAN trunk.

Which wins for each job

Job Beelink GTR6 Bosgame M4
Plex / Jellyfin ~5 streams win ~3 streams
Frigate NVR add a detector ~4 cameras win
Proxmox / VMs 24,021 PassMark 28,555 PassMark win
Firewall / router 1 NICs 2 NICs win
Local AI / LLM no slot no slot

Approximate - capacity estimates from curated specs, the same logic as the recommender. Verify against your exact setup. Prices move; check the retailer.

Full specs

Spec Beelink GTR6 Bosgame M4
Price (list) $449 $459
CPU AMD Ryzen 9 6900HX AMD Ryzen 7 8745HS
Cores / threads 8 8
PassMark 24,021 28,555
iGPU Radeon 680M Radeon 780M
NICs 1 2
NIC model Intel I225-V Realtek 2.5GbE
RAM max (GB) 64 64
M.2 free 1 1
PCIe slot none none
Idle (W) 12 13
TDP (W) 54 54