Are they really that much faster?
Yes, they are. A simple passmark puts the fastest Silvermont Celeron J1900 at 1885 and the slowest Haswell Celeron G1820 at 2866. That's not the whole story as the Silvermont has 4 cores and the Haswell only 2. Per core the Haswell chip is 3X as fast. In addition, the Silvermont GPU only has 4 EUs at 854 MHz and they are a generation older. The Haswell has 10 EUs at 1050 MHz. Not that you would be gaming on either GPU, but the Haswell one is much faster.
As an example, I have a new laptop with a Silvermont Z3775, passmark of 1328. It's basically a slower, lower power version of the Celeron J1900. My old Dell clunker with a Core 2 T7200, passmark of 1174 is still noticiably faster at end user tasks because it is much faster per core.
For a simple NAS the Silvermont is probably the better choice just for power savings. However, add anything CPU demanding and the Haswell is the better choice. It's not uncommon do do transcoding on a NAS like with PLEX and the Haswell would win hands down. In addition to speed, it has newer SSE support and Quicksync support which would help. The Haswell version also offers a much wider range of motherboards which can have more SATA ports if needed for more drives.
The right way to compare things is per Watt and per dollar at the same time, Atoms are way more power efficient and have much smaller max power usage than desktop processors, price is small too and if you care about noise, they are also fanless, another cost drop.
Things are not that simple. First off, the price is not much different. The discussed Asrock Q1900M Pro3 is $100 here. A Celeron G1840 (even faster than the G1820) and an ASRock H81M-HDS is $135. $35 gets you a much faster system and more SATA ports as well. You could probably cheap out on the MB a bit more and get the prices closer, but I wanted to make it comparable quality.
Second, power isn't so drastic either. At idle, the Silvermont would win, but not by much. For sure under 10W difference, probably under 5W. At load the difference would be more pronounced, but remember that the Haswell chip is getting much more work done for the watts used. A long running task such as video transcoding might actually be more efficient on the Haswell because it completes sooner. I don't know for sure in this case, but it was true for the older Atoms. They were so slow that they would actually use more power in the long run completing compute intensive tasks. Race to idle is a valid power saving method.
I think it's great actually, because people read too much not rational criticism of Atoms and don't buy them and I like to buy used stuff for half the price
I think Atoms are great in the right situation and I own several. However, anything compute intensive is not for them.