AVR based ones will be less expensive than Axon's, but if you needed a powerful avr based MCU already put together, the Axon is the way to go.
The Axon and Axon II is powered by an AVR 8-bit RISC MCU.
The Cortex series is good, but the ARM9/ARM11 core is better. Well, we could go on and on and on.
The main limitations of all the MCUs mentioned are memory (flash andRAM), and GP I/O (DAC, ADC channels, etc).
You can add some RAM (not EEPROM) to these MCUs but at the expense of I/O pins. Such is the world of embedded systems.
Best bang for the buck are the ARM processors.
- they are clocked fast (certainly faster than 16Mhz, I have an LPC2388 here clocked at 72MHz, another ARM9 clocked at 200MHz)
- have built in controllers for various peripherals (USB, SPI, LIN, CAN, MMIO, MAC, many other 3-letter abbreviated protocol, etc, etc)
- more built-in RAM/Flash than AVRs (almost 2x of AVR, ARM9 has MMU allowing you to connect a memory controller that can control DDR RAM)
- have more than 50 general purpose I/O pins
- 32-bits comes in handy most of the times (specially timers)
- mature toolchains readily available (Codesourcery for baremetal toolchains)
- ARM9 features data and instruction caches (better performance)
- has 16-bit instruction set (Thumb), in case you want to lessen the code size at the expense of execution speed
We can continue to discuss all of the good features of many MCUs but I guess it all depends on how much you want to spend, how knowledgeable you are with programming (and H/W interfacing), what features you want to use, and what other feature you may want to use in the future (expansion).
Goodluck.