Here's how I summarize my hatreds:
Early/Mid '90s Cowboys were an annoying rival but guess what, how can you be mad at a team that was gifted their greatness due to the Herschel Walker pick?? That team was ridiculously stacked on the OL and DL, making everybody around them better. To top it off due to Haley's inability to get along with Steve Young, he had to be traded.....although I have no idea in hell why they thought Cowboys was a good idea? Maybe the fact that they were 1-15 not many seasons prior, they were still seen as a bad team?
I've rewatched some of those games. The greatness of Steve Young and Rice is what kept us in those early bouts, then once we got over the hump I don't recall them beating us much, if at all.
Mid to late '90s Packers: Here's where I think I have more hatred for because it seems were we beaten more thoroughly. As has been pointed out by the sages on WZ, Holmgren and their DC just knew how to shut us down. Plus it didn't help that for most of this era we didn't have a good RB. Favre is more hateable than Aikman ever could be (then and now). Guys like Antonio Freeman, Mark Chmura were also annoying.
Cowboys games were close so to speak until late in the game when they would pull away. Packers games were frustrating from the 1st quarter on and never relented.
Mid to Late '80s Giants (early '90s Giants is misnomer here): A very interesting thorn in our side. A team that was built for the sole intention of keeping us out of super bowl appearances (then and now). Outside of 1985/1986 playoffs, they've managed to keep us out a few times by the slimmest of margins and luckiest of breaks. We killed a helpless '93 squad, and spoiled their '02 appearance....but those Giants teams were never going all the way. They are a perfect 5-0 in conference title games, two of which came at our expense.
You may say that if there wasn't holding on that Rice TD in '92 NFCC first drive the game could have been different, but those Cowboy and Packers teams that beat us were fundamentally better. The Giants teams that beat us after '86 have not been "better" once. So for that I hold them higher.
Plus like "NYVAGIANTSSUCK", I happened to live in the NYC metro area most of my life from 1986 onwards, so I have more real life Giants fan friends than Cowboys/Packers by a few miles. That part certainly does not help.
I'll have you guys know that Giants fans and even players from the late '80s always felt we dogged the Rams game in '88 finale to "keep them out" because we were scared and they also felt confident they could have beat us in '89 had Flipper Anderson not scored a walk off TD in OT the week before our 30-3 Rams beating. Even the '89 MNF game they felt they could have won, as I'm sure they would say about the '90 MNF the year after.
That sense of arrogant entitlement needs discipline. If I can paint the final Candlestick Park game with full control it's the Giants getting killed in the NFC Championship game.