All three versions are basically the same deck: solid, excellent sounding and arguably one of Sony's best and one of the best cassette recorders full stop. In 1983 Stereo Sound ranked it as Best Buy above the three monster Naks (Dragon, ZX-9, 1000ZXL). Not bad for a brand that "only makes nice Walkmans" !

The differences between the first non-ES version, the ES and subsequent ESII are as follows: the addition of a C Dolby NR (TC-777ES), the switch from S&F to Laser Amorphous Head, and a big change of main boards (777ES) ; the replacement of the FeCr tape position by an MPX Filter (previously located on the back), the disappearance of the remote plug (777ESII) and the addition of a 2nd power transformer.
Of course, the color changed as well: from the silver 777 to the "ES-magenta" (777ES) to the 1980s black (777ESII). The rest is the same : FET SEPP i/os, dual-mono boards, motor... and reliability & quality.
Sony made much of its reputation with tape recorders and the K777 was a fine example of this fact.