NES was the most powerful console at the time of its release...sure beat atari at least.
SNES was the most powerful console of its gen, not including add ons for other systems. It always had the best versions of a game, and it graphics were sharper, more detailed, and had more effects than the genesis or neogeo. Better looking 3d games too.
N64 was the most powerful console of its gen, it doesn't matter if psx could push more polys(which I'm not quite sure is true) you couldn't see most of them anyhow because the screen was extremely pixelated and low res.(I can't stand to play most low res n64 games too, mario 64 being one of the few exceptions) I hated playing psx on svideo, pixel popping and disappearing polygons all over the place.
As for framerates, I'll agree that psx tended to have more consistent framerates, but it was doing less, and I rarely recall any framerate problems when using software rendering back in the day(only in rare occasions, like in halflife's intro when everything goes to hell, and in quake when grenades explode, and that was on a 486 that I was using while my main pc was down anyhow), only with 3d acceleration have framerate fluctuations really seemed to pop up. Both systems had few 60 fps games, though psx did have more.
Conker's Bad Fur Day, imo, is one game that basically shows the full potential of the n64, high quality textures, sound, polygon counts, decent framerate, special effects, and all without the use of the expansion pack. Hi res n64 games were great....too bad there weren't very many of them, but super mario 64(not high res, but it had a simple clean look and a good framerate), perfect dark, conker's bad fur day, and maybe a few others are about the only games from last gen I can still stand playing on their home systems.(amazing how conker managed to do basically everything better than any other n64 game, and it had hi res, yet didn't use the 4 meg expansion)
If you tried to argue ds is more powerful than n64, maybe I'd give you that, its polygon rate totally eclipses the n64's, and it seems pretty good at texturing too. However, the psx's lead in polys, which at most may have been twice the amount, is too small to give the psx the lead in graphical quality.(though in many games, cds did make the difference, as did a smarter memory allocation) I just couldn't stand the psx's sliding textures and blurry pixelated graphics though. I remember in metal gear solid: vr missions, they had a high poly virtual mei ling to gawk at, but her hips and various other body parts would wave around and flicker in and out of existence! It was more nauseating than cute.
Gamecube would have been the most powerful without xbox...and it did launch in Japan before xbox launched anywhere, so it was the most powerful for a little while. Though in my opinion, nintendo crippled the gamecube by not giving it more video ram. If gamecube had say 16MB video ram, 24MB system ram, and that was it, I'd say it'd compare a lot better to xbox.
As for the handhelds....
Gameboy was the most powerful handheld, as it was the only handheld.
If gameboy color came out before neo geo pocket color, then it was the most powerful handheld at the time.(minus consoles turned into handhelds)
Gameboy advance was the most powerful handheld, and it may still be depending on how you look at it.....I haven't seen anything on gp32 that looks better than what gba can do, and gba beats the ngage in 2d graphics...plus niether of those are really competitors to gba.
DS will be the most powerful handheld period if it comes out before psp, and it may even be more powerful than the best pdas at the time.
I bet perfect dark 0/2 will be a launch game.
Oh, if we go by the logic that psx and genesis are more powerful than n64 and snes because their games ran smoother/had higher framerates(which was usually only true for exclusives compared to exclusives, not ports to ports), than gamecube is more powerful than xbox, there are more games that seem to be a consistent 30 fps on it, or 60 fps, than there are on xbox. Even xbox's star series, halo, can't maintain 30 fps in either game.
Nintendo doesn't make any great leaps in technology, but they are at where an industry leader should be when they launch a system. Gamecube is their only system that's launched at about the same time as another system, and its weakness could be explained by it being $100 cheaper and nintendo probably wasn't taking $200 in loses on it. Nintendo systems usually win on hardwired features though, and not raw power. Well, nes was raw power at the time, but snes did not have raw power, it had good features(not sure how to explain why its 3d games looked better than those on other systems though, maybe the fx chip was better?) and a sound chip and other chips to off load work, n64 was sort of raw power(most powerful cpu, may have been the most powerful graphics if you turned off all the effects, or were they hardwired?), gameboy advance wasn't raw power(has a graphics chip), and gamecube...well cpu may have the most raw power, but its graphics chip is easily the weakest, though backed with fast memory and hardwired effects.(wasn't it like 1 free light per texture layer?)
I kind of want to see gamecube 2 be an extension of gamecube's current graphics chip(just faster, more memory, and easier to use pixel shaders) just to see what gamecube could have done if nintendo had designed it better. On the other hand, I also want a console that can compete next gen graphically, so scrap the gamecube 2 idea.
NES, SNES, and N64 did have several years over the consoles they were more powerful than though.(well, I think there was an atari release around the time of the nes that sucked) Dreamcast did crush the n64 and only released 2-3 years later in Japan, but it was privy to a revolution the n64 had really caught hold of(the 3d revolution, n64 had 3d acceleration, that's about all you can say about it), plus I think if n64 was prefectly designed(no limitations anywhere, 64MB of system ram, a larger texture cache, fast cd rom drive, much faster ram, and just an overall better designed system only keeping the cpu and graphics chip the same could have competed with some of the dreamcast's earlier games, according to a nintendo press release I found online once, the n64 with a good microcode was capable of about 1.2 million polys per second, but with the crappy one the system launched with it could only do about 200,000)
Edit:
Anyone know why nintendo went for edram over just video ram like on a video card for gamecube? Isn't edram really expensive? Couldn't they have gottten more video ram at around the same speed if they went with external ddr, and if not, even the 6.4GB xbox had would have been more than enough for gamecube, something with voodoo5 level raw power doesn't need geforce 4 level bandwidth.