The verdict

CPU
Beelink SER5 Pro has 3.3x the CPU throughput (17,851 vs 5,333 PassMark).
Plex
Beelink EQ13 transcodes more 4K HDR streams (~5 vs ~3).
Idle power
Beelink SER5 Pro 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 Pro takes more RAM (64GB vs 16GB).

Which wins for each job

Job Beelink EQ13 Beelink SER5 Pro
Plex / Jellyfin ~5 streams win ~3 streams
Frigate NVR ~4 cameras win add a detector
Proxmox / VMs 5,333 PassMark 17,851 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 Pro
Price (list) $229 $239
CPU Intel Processor N100 AMD Ryzen 7 5825U
Cores / threads 4 8
PassMark 5,333 17,851
iGPU Intel UHD Radeon Vega 8
NICs 2 1
NIC model Realtek RTL8111 Realtek 1GbE
RAM max (GB) 16 64
M.2 free 1 0
PCIe slot none none
Idle (W) 11 7
TDP (W) 6 28