The only thing that would make me consider buying the BeagleBone Black Wireless is the two built-in microcontrollers ("PRU" processors [2]), for real-time I/O usage.
[2] http://beagleboard.org/pru
P.S. I'm not related to CHIP product, just a happy user :-)
Still, for $20 total outlay I have something that is between the Raspberry Pi B+ and 2 in performance, with arguably better expansion (if you value GPIO over USB), and a few nice extras like a power/reset button and built in support for LiPo batteries. The downside is that it's based on an Allwinner chip, and that company is known for being open-source hostile. Supposedly they are trying to improve, but it does limit the range of operating systems available for the device.
EDIT: I have too many of the little SBC, but in my mind the CHIP is outstanding value for these little projects where in yesteryears one would have used a microcontroller.
For things that need more power, I like the ODROID C2.
Soo many to choose from.
The specific CPU in the CHIP appears to have mainline support, so it's less terrible than things like the "Banana Pi M2+" ( http://linux-sunxi.org/Sinovoip_Banana_Pi_M2%2B ), but I like to support CPU manufacturers who aren't Allwinner.
First, the Bill of Materials for the BeagleBone is publicly available. I'm quite sure the BeagleBone guys would welcome your help in finding parts that are significantly cheaper than what they have now.
Second, the BeagleBone comes with a bunch of very standard connectors that are optional or hobbyist installs on a lot of the other boards. Ethernet jack, 2 usb ports (one OTG), an actual power adapter jack that isn't USB, both big headers already installed, mini-HDMI already installed, uSD card holder installed and probably a couple others that I forgot. Those connectors are not cheap AND they often have to be installed by hand.
Third, most BeagleBone's come with everything you need. You don't need to buy a USB cable. You don't need to buy a flash card. You plug it in and it powers up and you can do stuff on it. RPi's used to make you buy both a cable and a uSD card--maybe that has changed.
Finally, the BeagleBone is actually quite a bit more powerful and has more peripherals than most of these other boards. The BeagleBone always came with a processor capable of running stock Linux even from it's release in April 2013--the RPi didn't get that until the RPi2 almost 2 years later. Quite a few things on the BBB hang directly off the chip and have their own functional modules that don't conflict with other things. On the BBB, for example, Ethernet is wired to the chip--it does not suck up USB bandwidth like the RPi. While you can plug in a USB audio stick on the BBB, most capes actually access the McASP block so that they get direct DMA and again don't clog the USB bus. I can do a lot more things simultaneously on the BBB than I can on the RPi before bogging it down.
If you can use the RPi for whatever it is you are doing--great! It's a nice product. But there are a lot of us quietly using a lot of BeagleBones because it is way more powerful and had these things from the start. RPi adopted these things later and, funnily enough, needed to increase their price when they did so.
It's no coincidence that the RPi3 and the BeagleBone Green are almost identical in price.
This is my only nitpick with your post. While the Pi was in development, yes it was advertised as a "$25 computer", and once they finalized the design of the B version it ended up at $35. However, its price has not increased one penny since release, despite several revisions and huge leaps in performance and capability. Today we have the RPi 3, a quad core 64 bit computer that sells for the same price as the original single core, outdated-on-release board from 2012. If anything, that means the price has technically gone down, since you're getting so much more for the same amount.
Still true, at least when I got my RPi 3 from Adafruit a month ago.
The Allwinner CPUs are always extremely cheap, but I don't support the company because of what jerks they are to the open source community [2]
[0] http://elinux.org/Beagleboard:BeagleBoneBlack#Revision_C_.28...
[1] http://www.digikey.com/product-detail/en/seeed-technology-co...
[2] https://en.wikipedia.org/wiki/Allwinner#Linux_controversies
There are hardware design source files on https://github.com/beagleboard/beaglebone-black-wireless, including a PDF schematic: https://github.com/beagleboard/beaglebone-black-wireless/raw... which features a Texas Instruments WL1835MODGBMOCT WiFi/Bluetooth module: https://store.ti.com/WL1835MODGBMOCT.aspx