I have all three of them, but I have yet to play the Gamecube version since I just got back from my vacation yesterday, and still have a lot of other stuff to do.
On the original Starfox, I never felt that it was anything more than a below average game, it is a game I regreted buying after I did buy it. The N64 one on the otherhand, still to this day, remains one of my favourite action titles. The original one to me seemed more or less as just a graphics display with very poorly done clunky and boring gameplay. In other words, the SNES version is not a game I enjoyed at all; and usually I refer to Starfox 64 as the "first one" because I tend to subconsciously try to forget the original even existed =P
I have heard mixed feelings on the new one, some people love it, some people say that they like it, but that they liked Star Fox 64 much better. This place is probably the first place where I have heard of people liking the original the best; that opinion is in the vast minority I would assume.
One thing I have heard, I am not sure, is that the new Starfox game is very linear in comparisson to the N64 one which allowed many different paths to take. I'm actually not even sure of the nature of the new one, the N64 one was an action title, you played through to try and rank on the top charts or to try and acquire the various medals throughout the game. If the new one is linear, I would assume it is more along the lines of an action adventure.
Anyways, I'll probably play the new one today or in the next week, or so. On my trip I began Lunar Legend, and that game is occupying me right now (and yes, I do like that one better than the SSS Complete addition, I don't know why either, I can't justify it in my head other than maybe I'm always in a comfortable position while playing it =P I'm still only 7 hours in, so my opinion may change. The game is different than the complete addition even if it is the same world/setting/characters/towns and general story.).