The verdict

CPU
Beelink SER5 has 2.5x the CPU throughput (13,500 vs 5,333 PassMark).
Plex
Beelink EQ13 transcodes more 4K HDR streams (~5 vs ~3).
Idle power
Beelink SER5 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.
RAM ceiling
Beelink SER5 takes more RAM (64GB vs 16GB).

Which wins for each job

Job Beelink EQ13 Beelink SER5
Plex / Jellyfin ~5 streams win ~3 streams
Frigate NVR ~4 cameras win add a detector
Proxmox / VMs 5,333 PassMark 13,500 PassMark win
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 Beelink SER5
Price (list) $229 $259
CPU Intel Processor N100 AMD Ryzen 5 5560U
Cores / threads 4 6
PassMark 5,333 13,500
iGPU Intel UHD Vega 7
NICs 2 1
NIC model Realtek RTL8111 Realtek RTL8125
RAM max (GB) 16 64
M.2 free 1 1
PCIe slot none none
Idle (W) 11 7
TDP (W) 6 25