I bought the Fosi ZH3 a few weeks ago, but I returned it after just one day. Now I'm using the DX1 II. ZH3 is much larger and runs much hotter than the DX1 II.
ZH3 is not a bad DAC/amp. It's just that I have an easy-to-drive headphone (Focal Clear MG), so the extra power from the ZH3 is unnecessary for me. It only generates more heat with no real benefit in my case. The noise floor on the ZH3 is also slightly higher, so with sensitive headphones, the DX1 II sounds a bit "cleaner."
Moreover, the DX1 II is USB-powered, while the ZH3 requires a separate DC power supply. This means I have one less cable to worry about. Just connect the DX1 II to a USB 3.0 port, and it's good to go.
I pair the DX1 II with the JDS Labs Synapse MAX, and they work great together. Synapse MAX is a galvanic isolator that blocks noise from PC. Synapse MAX also delivers enough "clean" power (up to 5V/1A) for the DX1 II.
I really can't complain about my current setup. But in the end, it still depends on your headphones and whether you actually need the extra power.
If power is not an issue, the DX1 II offers the best functionality, for sure. It has a remote control, a better display than the ZH3, and can be controlled from desktop using the Web Control Center.
Edit: Remove "ground loops" from the paragraph.