Purely speculative, but I think using phoenix allows an instance of the miner for each GPU. Thus you can can monitor each process independently. You can then kill and reload that specific hung process through the OS whereas cgminer doesn't quite offer the high level monitoring/control. If a card hangs in cgminer, you're at the mercy of cgminer to recognize the fault and try to re-initialize that card. From my experience with cgminer, if this occurs it generally means a full system hang, but I've not played with phoenix to see if a hung process operates in a similar manner.
Nothing prevents you from launching a separate cgminer instance for each of your GPUs.
The issue with AMD cards from 6xxx generation onwards is that when they go down, they usually go down hard - not only will you be unable to resurrect them but if it is the system's primary
(1) GPU that dies it can effectively take the whole system down by introducing freeze periods of a few dozen seconds each time the kernel is trying to access the non-responsive card.
Luckily,
reboot -f has worked quite reliably for me, though situations where cycling the power was necessary have been reported in these forums.
Notes:
(1) usually closest to the CPU socket unless GPU ordering is changed in BIOS