I have not listened to any of the two, but I would not expect them to have a different timbre being similar level units and made at about the same time. The 8080 is perhaps a bit more robust with twin transformers and a more substantial power supply. It also offers a pre-out/main-in set of connectors that can be very handy if you ever want to connect a sound processor (equalizer, etc). Also offers capacitance and impedance phono load selection (hi/low) as was the fad in the day.
The 8077 offers MM/MC phono inputs that may be of relevance if you are into turntables and into MC carts. The VF power display is just a gimmick that looks impressive to some and perhaps has a more versatile source management arrangement, in that you may be able to listen to a tape or CD and record an LP to a tape.
Of the two (if I could not get both) I would choose the SU-8080 because it's heavier (better power supply).
To make my response more technically sound,
The 8080 is rated for 2x72WRMS @ 8ohm and 2X90WRMS @ 4ohm
The 8077 is rated for 2x60WRMS @ 8ohm and 2x65WRMS @ 40hm (shows a power supply limitation).
Now, while the difference between 60, 70 and 90 watts is not much, the 8080 will be able to drive speakers much better and cleaner at higher volumes.