We use Cisco and like it well enough... but I don't have any experience with Avaya. Cisco has lots of features and flexibility... however our phone person stated that she liked the Avaya better as it's less complicated than the Cisco solution.
Call Managers, Voice Gateways, and Contact Center have A LOT of pieces that all have to come together perfectly or calls can be dropped, hung in the system, etc. It also relys on Java some, which I'm not always 100% fond of. I'm completely comfortable with the Contact Center piece, however Call Manager and VG's can get pretty confusing if you're just used to "normal" networking, and I try to avoid it :-). Cisco may have smaller solutions which are more simple to deploy... ours have probably around a thousand phones, HA, multiple locations around the world and require the contact center to prompt in various languages, multiple tiers for agents, routing based off of database dips, for a 24/7 facility... so it's probably not the most straight forward... but I will say the Cisco stuff seems "needlessly" complex... again I can't compare it to Avaya since I haven't worked with it... but maybe something to keep in mind when reviewing the two.