around 2002, why the hell do you ask?

I was just a kid, and I was oblivious to console wars back then. My older brother owned both consoles and I would just play whatever games that were available. If only I could have maintained that innocence.

OP, I'm going to attribute my choice of greatest rivalry to my own personal experience- the moment it finally dawned upon me that consoles of choice created something ugly known as console wars . mid to late 90s, PSX vs N64. God I can still remember classmates fighting over what was better during lunch. It just got ugly. It came down to if someone owned one or the other, that was the better console and the other person was stupid for owning the opposite. Even if you were casually talking to someone and mentioned a console you would get snarky remark about it.

I guess the next war was Dreamcast vs Gamecube vs PS2, but I was safely living overseas in that time, away from the cruel console battles ( I didn't even realize sega was still releasing consoles at this point, shows you how much I know).  But Only to come back to the current console wars, that I'm a part of. I wish I never visited this site in 2007!

*reads Hatmoza's comment*

An child whose innocence was claimed by the fires of a lifetime of war. Tragic. Sometimes I wonder if video game manufacturers even realize the harm they've caused.

I know people who were around during SNES vs Genesis - if it's even half as insane as they say, then it's definitely the greatest console rivalry.

It's not a rivalry if you lose. SNES sold a clean 20 mil more consoles than Genesis, and more than twice as much software. Hey, I loved that gen as much as the next guy (I was a Genesis owner myself), but that rivalry -- while legendary -- was extremely unbalanced compared to the 360/PS3 rivalry of today. The growing number of multiplatform games is fuel for the fire -- not only do fans simply debate which exclusives are better, but which version of the same game is superior. These battles are fought primarily on an entirely new battleground: the internet. Heated discussions between friends have made way for lengthy arguments between total strangers. New weapons and targets complicate fandom warfare: screen cap comparisons, hardware durability, network security, cost effectiveness. DualShock vs a knockoff. Move vs Kinect. RROD vs PSN hack. XBL vs PS+.

For sure, SNES vs Genesis is the only one that comes close. But PS3 vs 360 is going down to the wire. It's at least closer, if not more heated, than the 4th gen war. One inhibitor to the current-gen war is the number of gamers who own both consoles and appreciate the strengths and weaknesses of each.

SNES vs Genesis hands down.
I used Streets of Rage 2 as a training tool to beat the hell out of the SNES kids at school. It was more than a rivalry... It was war.

So ... World War II didn't happen because the Allies won?  I hope you understand how silly that is. 

SNES ended up with a big lead but most of it was simply by outlasting the Genesis.  Although, to be fair, [edit:  the Genesis] also had a head start, so you could say the whole battle was one of the SNES trying (ultimately successfully) to defeat the Genesis, which was then in the process of defeating the NES.  But believe you me, the rivalry was there.  Did you even look at the videos lewis posted? 

ZX Spectrum vs Commodore 64 was the best school playground war, the sheer power of the Commodore against the four colours fool, i remember having a few arguments and fights with some kids when i was at school back in the 80's, It's too bad that only 16 C64 games ever got released on the Wii's virtual console.

Only the rich kids had Vic20s.

SNES vs. Genesis.

In (distant) second, the Wii vs. gaming journalists.

I was going to correct you on that and say the MegaDrive launched before SNES, but I think that's actually what you meant. (The sentance doesn't read like that to me though)