The verdict

CPU
Beelink EQ12 has 1x the CPU throughput (5,500 vs 5,385 PassMark).
Idle power
Beelink Mini S13 idles lower (6W vs 7W) - cheaper to run 24/7.
Networking
Beelink EQ12 has more NICs (2 vs 1) - better for a firewall or VLAN trunk.
RAM ceiling
Beelink EQ12 takes more RAM (32GB vs 16GB).

Which wins for each job

Job Beelink EQ12 Beelink Mini S13
Plex / Jellyfin ~5 streams ~5 streams
Frigate NVR ~4 cameras ~4 cameras
Proxmox / VMs 5,500 PassMark win 5,385 PassMark
Firewall / router 2 NICs win 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 EQ12 Beelink Mini S13
Price (list) $189 $189
CPU Intel N100 Intel Processor N150
Cores / threads 4 4
PassMark 5,500 5,385
iGPU UHD Intel UHD
NICs 2 1
NIC model Intel I226-V Realtek RTL8125
RAM max (GB) 32 16
M.2 free 1 1
PCIe slot none none
Idle (W) 7 6
TDP (W) 6 6