Just to clarify the differences, the Zbox and similar small computers like the Intel NUC are not really standardized like the ITX form factor. ITX is a full-power desktop in a small package with a standardized motherboard layout, meaning you can buy an ITX motherboard from any company and it will fit any ITX case - not so with the Zbox or NUC.
The Zbox you linked is actually quite fast compared to similar small form factor computers, however the CPU is still less powerful than your i7-4770, though only by about 2%. By comparison the ITX computer I'm building is around 2.5x as fast with the i5 I'm using, or up to 3.5x as fast if I were to use an i7 or i9. Of course it's much bigger though - the case is just over 3" thick and around 15"x13".
Storage speed is probably more of an issue than CPU speed - from the looks of it, the Zbox only supports SATA SSD's and not PCIe/NVMe. ITX or the NUC platform would be much faster in that respect, as SATA tops out around 550mb/sec where NVMe currently tops out at 7300mb/sec which is 13x faster.