The verdict

CPU
Beelink Mini S13 has 1x the CPU throughput (5,385 vs 5,307 PassMark).
Idle power
Beelink Mini S13 idles lower (6W vs 8W) - cheaper to run 24/7.

Which wins for each job

Job Beelink Mini S13 Trigkey Green G4
Plex / Jellyfin ~5 streams ~5 streams
Frigate NVR ~4 cameras ~4 cameras
Proxmox / VMs 5,385 PassMark win 5,307 PassMark
Firewall / router 1 NICs 1 NICs
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 Mini S13 Trigkey Green G4
Price (list) $189 $189
CPU Intel Processor N150 Intel Processor N100
Cores / threads 4 4
PassMark 5,385 5,307
iGPU Intel UHD Intel UHD (24 EU)
NICs 1 1
NIC model Realtek RTL8125 1GbE (chip unlisted)
RAM max (GB) 16 16
M.2 free 1 1
PCIe slot none none
Idle (W) 6 8
TDP (W) 6 6