Different design decisions.

Just look at the hardware and you have your answer.

Well, it's arguable the power difference is overblown. Take Tomb Raider. The internet has made it out that the XO version may as well be the Commodore 64 version. But go look at any given shot in DF's comparison gallery, compare to PS4, and they are likely to be identical . Sure there are a few visual differences between some of the screens, but they're few. Of course their is the framerate too, but even that isn't a true story of average 30 vs 50  because the XO version is handicapped by a 30 FPS cap. And anyway, really few people notice the difference between 30 and 60 to begin with (that's why it's mostly relegated to certain genres).

The same type of thinking applies to the other games where there's a difference. I challenge you to go watch split screen youtubes of BF4 on X1/PS4 and notice much difference. Even though the PS4 is pushing 50% more pixels, the onscreen difference it actually makes is more like 5%.

Basically your average uneducated Joe walking through Wal Mart is going to notice little if any graphical difference between PS4/XO. And that validates MS's claims the difference isn't that large.

PS3 often was well behind 360 multiplatforms perhaps even by similar amounts (lower framerates, lower resolutions, etc), yet you didn't see the huge backlash with each and every inferior multiplat against PS3 that you're seeing with X1. So anti-Microsoft internet bias plays a part too.

Now, to more technical answer to your 2nd Q, how MS could make such a mistake...well again I think you're vastly overblowing the power gap. But basically MS just aimed low, and yes, that was indeed stupid. They probably still would have been fine if Sony hadn't upped PS4 from 4GB to 8GB at the very last second, though.

MS basically went for an architecture with a lot of on die ESRAM, which somewhat limited how many shaders could fit. In return for this, they were able to use much cheaper DDR3 than the expensive GDDR5 Sony is using. The overall cost to build a Xbox One minus Kinect, is less than PS4, a lot less.

Yet Xbox One is still $100 more, which is a problem. Two reasons, foremost is Kinect, which is a strategy decision on MS's part. They thought the allure of Kinect would be greater than it has been so far. You can argue till the cows come home about it. But Kinect is expensive hardware.

Second reason, simple profit. Sony is losing some money on PS4 hardware, Microsoft is likely break even or better on XB1. If MS was willing to lose some money on XBO hardware as Sony is on PS4, then they could price it lower. But so far they dont.

Oh also, it's worth noting XBO build quality is quite a bit better than PS4, which contributes to the expense. It's bigger, quieter, more solidly built, and the PS4 controllers are having issues falling apart such as the thumbsticks. This is a somewhat minor factor compared to the others, probably not a huge difference, but still worth considering, that sony shaved a few bucks there as well.

Also I'm not sure what you mean PS3 came a year after 360 so the power difference was justified. 360 was more powerful than PS3 in multiplatforms, and I think Halo 4 looks as good as any PS3 exclusive. If anything, I found it terrible engineering by Sony they came out a year later and didn't blow 360 away. They had a golden opportunity there and blew it. When Xbox came out a year after PS2, it blew PS2 away (in power). But Sony was not able to do the same with PS3 vs 360. So Microsoft have generally been the superior engineers. Xbox One is weaker than PS4, but that was a strategy/budget decision by the suits not bad engineering.

Overall I still say XBO will be fine in the long run. Microsoft have been incredibly non-aggressive on price which is annoying, but oh well. That is why Microsoft is filthy rich and Sony's debt was recently downgraded to junk status.

The DDR3 base of the XBO will allow it to cost reduce faster than PS4, and once they reach price parity or XO is priced lower than PS4 it'll be fine. It's powerful enough. Everybody is ripping the hardware but yet it's considered part of "next gen" with PS4, getting all third party multiplats, which was the point, and really the only goal MS couldn't screw up. A disaster would have been if it was closer to Wii U, and devs refused to port to it. That's simply not the case.

Nintendo, Microsoft and Sony all sat in a room and agreed to make their consoles similar in power. Sony lied.

Sony is the kind of guy (Yes, Sony is a guy) that agrees to spend $50 on a Christmas present and while you're there giving a gift certificate to Gamestop, they're giving the keys to a new car. Asshole.

The raw specs of both are enough to run 1080p and 60fps. Not in all games obviously, but the argument that the XB1 isnt capable because it is weak is silly. Any multiplat that runs at 1080p on PS4 has that same potential on XB1 when properly optimized. Whether XB1 has the same effects such as particles, filtering, shadows, textures .... is another story.

Having esram a slight boost but when you have outdated drivers.......its a major annoyance.

XB1 launch games have been plagued with last minute changes to hardware speed and outdated drivers.

As the dev tools get updated and optimized, XB1 will be running 1080p with no problem. Whether the framerates are as fast as PS4 is another issue.

The PS3 overall was not more powerful for gaming than the 360. It had a stronger processor, but that was bottlenecked by awful memory management and a weaker GPU. Get the facts right.