All the rumors are clearly stating that the Cafe is at least a third or more stronger than current-gen consoles like the PS3/360.
With how expensive development costs are, the limitations set by a console's resolution, current storage problems that devs are running into, and Sony's current inability to support a complete push like they gave the PS3, NO, PS4 is not gonna be "hella more powerful".
The power difference between Cafe and PS4 will be nowhere near as grand as it was between Wii/PS3. Sony simply cannot afford something that bleeding-edge, at least not again. No one said it would be weaker though, you interpreted that on your own.
As for Cafe's release timing, how is it awkward? It is releasing at least 12-18 months before the consoles of the competition, with HW specs that may not necessarily get "stomped" by the time the 720/PS4 actually do release.
If Cafe is only a third more powerful than a PS3, that means it'll place in roughly the same way, hardware-wise, as the Wii over the PS2/GameCube--as in, it won't be substantially more powerful than current-gen machines. It might get some 3rd party ports of Xbox360 and PS3 titles, but the second Microsoft and Sony launch their systems, 1-2 years later, Cafe won't matter any more. It'll be the Wii all over again.
It'll be a system that isn't powerful enough to handle the engines of the next generation that are optimized to run on the X720 and PS4. In much the same way the Wii got nothing on the current Unreal engine, Cafe won't get anything for the Unreal engine made to run on X720 and PS4.
Project Cafe needs to be actual next-gen technology, and if it's only a measly third more powerful than the X360 or PS3, then that means Nintendo's next-gen system is made with current-gen technology again. The PS3 isn't only a third more powerful than the PS2--it's several times more powerful.
The timing will be awkward--Dreamcast awkward. Coming out before this generation is finished, and before the next is truly ready to go. It'll sell mostly to just Nintendo's core fans, that that'll be it. When the PS4 and Xbox720 launch, Cafe will look like generation-old technology, just as the Wii did. The Dreamcast launched 12-18 months before it's competition. First to market is never first in sales. The difference is that Nintendo didn't burn bridges with the Wii the way Sega did with the Saturn (Sega-CD and 32X), so Cafe might not end up being their last console--but it certainly isn't on track to be a success.
Asuming the PS4 won't be drastically more powerful than the PS3 is just silly. Obviously it'll be drastically (hella, if you like) more powerful, otherwise there'd be no reason to do it. Just like the next Xbox will be drastically more powerful than the X360. They won't be a laughable "third more powerful." They'll be a good three to nine times (or more) more powerful than the current gen machines. Again, like the Xbox360 over the Xbox. Sony said they're going to be more mindful of the cost, that doesn't mean they're going to make a weak-ass console. They're going to make another powerhouse, but be more mindful of the way in which they do it.
Nintendo aiming low (hardware tech wise) like they did with the Wii earned them a lot of laughs, little 3rd party support, and even fewer ports of popular multi-platform titles. If Cafe is truly only a third more powerful than the Xbox360 or PS3, it's a "next"-gen system with last-gen appeal. Either it's a true current-gen system releasing too late to matter, or it's a next-gen system barely any more powerful than current-gen systems. And it'll launch a good year or so ahead of Microsoft and Sony's next machines, which means any success it has will be short lived as they'll have time to properly capitalize on Cafe's successes.
Cafe isn't going to set the gaming world on fire. Especially if the rumors of it's strength are true.