Tyrolia's always have been solid.. Didnt ski the new AAAtack yet but it would suprise me if it wasnt as solid as the last years models.. Those bindings are also rebranded by a lot of companies, so pretty safe choie..
With marker I personally have had a bad experience, but that was a few years back.. They prob solved that..
Go for the cheapest/best color combo with your skis/best service you can get when you do have a problem with your bindings..
'A wise man will make more opportunities than he finds'
As said whilst the old Peak series bindings weren't the best selling bindings on the market, they seemed to get their fair share of praise. I haven't skied Griffons, I've only skied Jesters, but I haven't had great experiences with my markers. However it is hard to compare them to the new Tyrolia bindings, as few people have skied the new Tyrolias. If you do decide to go down the Grifon route try to find a pair of the 2010/2011s (the White/grey/red ones), that year was the last year with a more substantial amount of metal in the binding.
The Tyrolia AAA had some components redesigned for the 13/14 winter I think they've brought down the weight to be competitive. Some people complain about the Marker touring mode lever being under the boot, others prefer it.