Welcome to the forum acstolinker

Q. Is the noise rating always of primary importance?
A. A lower noise rating allows you to receive weaker signals. You want your first stage of amplification to be as quiet as possible because all subsequent stages of amplification will in turn amplify the noise from the first stage.
Q. Is it possible that the NEW 7777 may be better in some situations because of its higher gain, despite its much higher Noise rating?
A. Higher gain is only helpful to a point. Beyond that, it significatly increases the odds of overloading your tuner. The higher the gain, the further you need to live from the transmitters and/or the more system loss (cable length & splits) you need to have. For example, the current 7777 is recommended if you live at least 20 miles from most of your transmitters. Thus, with both a higher noise level and a greater potential for overload, the new model is probably not going to be as helpful. Additionally, it only has one input and one amplifier.
The current model has separate inputs and amplifiers for VHF & UHF. These facts may explain the number of views of this thread to date.
Q. I know my Signal-Power and Noise-Margins for each channel at my particular location from my TVFool plot, I can calculate my system losses from antenna to tuner, but how do I use all this to determine if it's pre-amp gain or pre-amp noise that will make or break my application?
A. See holl_ands web page:
http://imageevent.com/holl_ands/files/ota He is very knowledgeable on this subject.