The ethernet card is very similar to an outboard M5 and is internally connected via I2S. This provides stellar clocking between the player and DAC. That is why it outperforms many other options.
With my Antipodes K50 I was able to test Ethernet from the server half of the device, AES and Coax from the on-board clock and the USB which is obviously asynchronous. The K50 via AES Coax beat the Ethernet. It was closer than I would like it to be given the card costs $1000 and the player/clock half of the Antipodes is like $7500 to buy on its own plus you need a server. The ethernet synchronous inputs were noticeably better than the USB.
An elite server and player can beat the ethernet card but at a price ($17.5K) that most consumers would not spend when paired with an M3. Given how strong the ethernet connection is via the Bricasti, I think the most logical solution would be to run a high-powered server that can handle those 6TB of data and not burden it with player duties.
My suggestion would be to look at the Antipodes S40. It can handle up to 8TB of data and offers a direct ethernet streaming connection from the device. This would allow you to continue to leverage the ethernet card and have a nice, high-powered server that can easily handle a big and demanding library. It also bypasses your router and other equipment in terms of connection between server and DAC after signal processing has begun.
Full disclosure, I am a Bricasti and Antipodes dealer. I would also say I have not tested Innuos, EVO and other devices that solely use USB outputs and have no comment on how they might perform differently.