The verdict

CPU
Beelink GTR6 has 5.6x the CPU throughput (24,021 vs 4,300 PassMark).
Plex
Beelink GTR6 transcodes more 4K HDR streams (~5 vs ~4).
Networking
ASUSTOR Flashstor FS6706T has more NICs (2 vs 1) - better for a firewall or VLAN trunk.
RAM ceiling
Beelink GTR6 takes more RAM (64GB vs 16GB).

Which wins for each job

Job ASUSTOR Flashstor FS6706T Beelink GTR6
Plex / Jellyfin ~4 streams ~5 streams win
Frigate NVR ~4 cameras win add a detector
Proxmox / VMs 4,300 PassMark 24,021 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 ASUSTOR Flashstor FS6706T Beelink GTR6
Price (list) $450 $449
CPU Intel Celeron N5105 AMD Ryzen 9 6900HX
Cores / threads 4 8
PassMark 4,300 24,021
iGPU Intel UHD (24 EU) Radeon 680M
NICs 2 1
NIC model Realtek RTL8125 Intel I225-V
RAM max (GB) 16 64
M.2 free 6 1
PCIe slot none none
Idle (W) 12 12
TDP (W) 10 54