The processor is an Xtensa lx106 made by Tensilica in China. This is a unique processor, but it is well supported by a gcc toolchain.
The most limiting factor is RAM. There is 64K of instruction ram and 96K of data ram.
Compare this to a typical 8 bit AVR controller like the 32u4. This is a miserable 8 bit processor running at 16 Mhz with 2.5k of ram and 32K of flash. You should realize that you can ignore or turn off Wifi on the ESP8266 and have a very capable microcontroller for as little as $2.00. This makes it very hard to work up any interest in any AVR based product, even the most inexpensive and sleek ones (such as the Sparkfun 32u4 based Pro-micro for $20).