The verdict

CPU
Beelink EQ13 has 1x the CPU throughput (5,333 vs 5,307 PassMark).
Idle power
MeLE Quieter 4C idles lower (7W vs 11W) - cheaper to run 24/7.
Networking
Beelink EQ13 has more NICs (2 vs 1) - better for a firewall or VLAN trunk.

Which wins for each job

Job Beelink EQ13 MeLE Quieter 4C
Plex / Jellyfin ~5 streams ~5 streams
Frigate NVR ~4 cameras ~4 cameras
Proxmox / VMs 5,333 PassMark win 5,307 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 EQ13 MeLE Quieter 4C
Price (list) $229 $220
CPU Intel Processor N100 Intel Processor N100
Cores / threads 4 4
PassMark 5,333 5,307
iGPU Intel UHD Intel UHD (24 EU)
NICs 2 1
NIC model Realtek RTL8111 1GbE (chip unlisted)
RAM max (GB) 16 16
M.2 free 1 1
PCIe slot none none
Idle (W) 11 7
TDP (W) 6 6