Bit Depth:

For selecting color mode.

Gamma Correction:

Very extensive Gamma options of the Twin Turbo.
Allows adjusting monitor gamma to match printed output.

General:

Allows disabling of general & text* acceleration,
useful on all text web pages for instance.
(* indicates disable feature not found in Hawkeye)

Resolution:

Allows setting the screen resolution without opening Apple's monitor control
(not found in Hawkeye control).

Pan/Zoom:

Settings for Pan and Zoom.

The Twin Turbo lacked some of the features of the Hawkeye control,
but did have some exclusives of its own, like setting the resolution
without using the Apple control, and the ability to turn off text
acceleration.

The Twin Turbo has a very nice feature set,
but I still preferred the layout and features of the Hawkeye.