Assuming they each are sold for a slight profit at $199.99 without expensive new features, what type of power range can we expect from them?

Slightly worse than XBO for home console if smart parts were chosen. Moderately more powerful than Vita if the right parts are chosen. The way Nintendo builds hardware though probably means the 'right' parts won't be chosen.

They'd be pretty underwhelming, probably even compared to the PS4.

Handheld should be like 10 times more powerful than 3DS. HC depends on architecture but for that price it can't get much better than wii u.

If not sold a significant loss, you are looking at about maybe a portable Wii U for handhelds and for a home console something just slightly better pretty much on par with the GC to Wii jump in terms of potential.

If it is released next year, which would mean it is all but finalized in terms of what hardware it will have under the hood. If they have breathing room and nothing is finalized until mid next year with a late 2017 release target then their is small room for tiny jump beyond that closer to PS4 or Xbox One capabilities but still a tad slower.

If the console was only $200, I'd expect it to have less power than the Xbox One

For the handheld, it should be around the Vita

I wonder if they will sell it in parts. The "full" package where you get the home console that streams / downloads games to the handheld console, and separate packages with the home console alone or the handheld alone where every game would be digital distribution only.
Therefore they could charge $400 - $500 for the full monty, or divide that up for the smaller packages.
I think they will try to have the handheld run the same games that the home console does, but at a much lower resolution. This however means that the home console won't be anywhere near as powerful as we may have hoped.
Or..... I'm totally wrong who knows! Bring on E3 2016

I don't understand why some people expect only a GC to Wii jump for the console, there are plenty of options out there that are both reasonable, and provide a moderate jump in raw power. The R7 250X for example has 640 shaders (at 1ghz it's a little over 1 TF) and under mass production, will run well under a hundred USD alone, and we'll likely say good-bye to the PowerPC CPU once and for all as a central processor hopefully (will be funny if we end up with 8 Espresso cores). Wii U's processors were likely chosen around 2009 (console form was decided in April 2009, and the GPU is 2008/2009 tech), the console this time if it's launching 2016/2017 will have likely have had their processors chosen already (2013/2014 tech). There's literally no reason for them to only have a 1.5x Wii U jump even if they're targeting $199.99. A 640 shader GPU may not be at PS4 power, but it's doable at a decent price without an expensive gimmick and will make them profits. At $249.99, maybe we can expect a 768 shader part instead, which at 1Ghz would put it around XB1 power. I know we expected a lot from Wii U and ended up with a rather weak machine, but it was still significantly more powerful than Wii. Why people expect an overclocked Wii U for the NX console is beyond mii...

The handheld has no problem significantly surpassing the 3DS, though I don't expect a 199.99 price tag. If NXDS is released next year, at $149.99 we can expect something moderately better than Vita in power...as long as they don't have some expensive gimmick.

The issue isn't so much the price alone, it's likely the fact that Nintendo will fall in love with mobile components and their low power consumption.

Using the same family of mobile chips will allow them to share console/handheld library, but it will also likely hold the console variant (assuming there are two+ versions) back.

I'd guess 300 GFLOPS with 3GB RAM for the handheld with a cheap-ish screen (1280x720, which is good for Nintendo standards).

800 GFLOPS using the same type of mobile components for the home version, just juiced up with 4-5GB RAM. New controller type in the box, not an expensive controller however.

But it's not like you couldn't get something powerful for $200 these days, a 2.3 TFLOP GTX 960 is easy enough to find at $199.99, and yes while that doesn't include a CPU, you also have to take into account that component is marked up for retail and manufacturer profit margins, a buyer like Nintendo could get a component like that for cheaper. Also factor in we're talking about a launch window that is likely almost a year and a half away. 

I cant see why you think home and handheld consoles will have same price.

Handheld probably pretty stronger because 3DS i so weak and next handheld will need to have much better resolution screen.
Home console probably little less powerful than Xbox One.

Thats if we assuming that NX is home and handheld console, but I think it one hybrid device with power somewhere between Wiiu and Xbox One.