In addition to Intel ME there was a controversy over microcode updates: an exploit was demonstrated on Blackhat 2015, and few academic papers with similar security evaluation were published by several people even before that.
http://techreport.com/news/28784/vu...intel-cpus-gives-away-the-keys-to-the-kingdom
https://www.dcddcc.com/docs/2014_paper_microcode.pdf
I believe Intel ME is still on the chipset. Though the way it works is exactly the same, and there were a bunch of papers written on possible implementation of such exploits.
Those are completely different use cases. There are ARM cpus everywhere, but they are used either as Central Processor, or peripheral processor. AMD plans to use it as secure boot mitigator, which means the following:
1) you have no control over it, and you probably can't monitor it beyond passive observation and firmware reverse-engineering. Being inside of a CPU (just like ME is a part of chipset), only makes things more complicated
2) this ARM core is the first thing to start and have access to all system resources. Nothing prevents it from injecting sub-routines on BIOS level, altering a bootloader, or observing/manipulating your hardware without you knowing it.
3) An external flash for this chip will most likely run on an SMBUS or SPI with many other devices, so exploiting the new secure boot system will be just as easy as updating BIOS on your GPU. Using deceptive techniques may provide hackers with an easy way to create an army of zombies.
https://www.contextis.com/documents/93/CRESTCon_-_Exploiting_hardware_management_subsystems.pdf
https://www.blackhat.com/us-16/training/applied-physical-attacks-on-x86-systems.html