The verdict

CPU
HP EliteDesk 800 G6 Mini has 1.9x the CPU throughput (10,221 vs 5,385 PassMark).
Plex
Beelink EQ14 transcodes more 4K HDR streams (~5 vs ~3).
Idle power
Beelink EQ14 idles lower (6W vs 11W) - cheaper to run 24/7.
Networking
Beelink EQ14 has more NICs (2 vs 1) - better for a firewall or VLAN trunk.
RAM ceiling
HP EliteDesk 800 G6 Mini takes more RAM (64GB vs 16GB).

Which wins for each job

Job Beelink EQ14 HP EliteDesk 800 G6 Mini
Plex / Jellyfin ~5 streams win ~3 streams
Frigate NVR ~4 cameras ~4 cameras
Proxmox / VMs 5,385 PassMark 10,221 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 EQ14 HP EliteDesk 800 G6 Mini
Price (list) $189 $185
CPU Intel Processor N150 Intel Core i5-10500T
Cores / threads 4 6
PassMark 5,385 10,221
iGPU Intel UHD UHD 630
NICs 2 1
NIC model Intel I226-V Intel I219-LM
RAM max (GB) 16 64
M.2 free 1 1
PCIe slot none none
Idle (W) 6 11
TDP (W) 6 35