The pros for the Yammy are:
7.2 (MRX doesn't have .2)
7 HDMI connections
Upgradeable to 9.2 (just in case)
The Yammy will most likely have superior specs in cross talks, S/N, THD etc. Historically their mid range RX-V series did offer very clean and quiet preamp sections. They also seem to be top notch in terms of reliability.
Pros for MRX300:
Anthem!!
ARC
I am not sure why those are "pros". I like my Anthem amp too, but I don't think it is necessarily better than other amps, and the MRX300 is just their enty level AVR. I would really like to see some professional reviews on ARC, until then it is all hearsays. It may or may not be better than YPAO or Audyssey.
I dont really know about video processing or anything like that. WOuld there be a massive difference between the 2?
I find VP a waste of time. If you have a decent TV and BDP, even something like a PS3 and/or a $150 sony such as the 470/570, they will most likely do a better job than those two AVRs. If you are thinking of using the AVR to upscale analog signals from VCR or streaming sources etc., you won't get good quality video regardless. All the VP in the AVR can do is perhaps a little bit of noise reduction, nothing else. I tried all sorts of combinations, in the end I know the best thing to do is to turn off upscaling. So to me it is not a factor at all.