The verdict

CPU
HP ProDesk 600 G5 Mini has 1.5x the CPU throughput (8,038 vs 5,500 PassMark).
Plex
GMKtec NucBox G3 transcodes more 4K HDR streams (~5 vs ~3).
Idle power
GMKtec NucBox G3 idles lower (6W vs 11W) - cheaper to run 24/7.
RAM ceiling
HP ProDesk 600 G5 Mini takes more RAM (64GB vs 16GB).

Which wins for each job

Job GMKtec NucBox G3 HP ProDesk 600 G5 Mini
Plex / Jellyfin ~5 streams win ~3 streams
Frigate NVR ~4 cameras ~4 cameras
Proxmox / VMs 5,500 PassMark 8,038 PassMark win
Firewall / router 1 NICs 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 GMKtec NucBox G3 HP ProDesk 600 G5 Mini
Price (list) $139 $135
CPU Intel N100 Intel Core i5-9500T
Cores / threads 4 6
PassMark 5,500 8,038
iGPU UHD UHD 630
NICs 1 1
NIC model Realtek RTL8125 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