I recently purchased the TX-NR616 - a few weeks back. I haven't ran into any issues, although I have read the 'horror stories' out there. It does seem that the product launch for Onkyo's 20112 receivers have not been kind to the customers, nor themselve's (especially with customer support). Just make sure to update the firmware from the start and I think that will solve most issues. I know some of the issues are from recent purchasers, such as myself, but it seems like others are from earlier adopters that had the much earlier shoddy firmware and have struggled through everything up until 'today'.
Anyhow, like you, I was considering a Denon (about twice the price of the Onkyo), but I thought I would give the 616 a shot mainly for the ridiculous feature-set (8 HDMI, THX cert, etc.) for the low price, and I can tell you that I am extremely satisified. The network features are great, and even better than the Denon models, including the selection and GUI. While AirPlay is not there right now, it could potentially be with a firmware update if Onkyo licenses it. With that said, an AppleTV though is probably the better choice for such a task (and will also include video - including iOS device/Apple computer screen sharing. The AirPlay found in AVR's are audiio only). You can also check out AirMusic that will transmit your music over DLNA from your Apple device: http://itunes.apple.com/us/app/airmusic/id409782234?mt=8
Actually, thinking about it more, probably the main reason I went with the Onkyo is because the dealer I went to no longer carried Denon, due to contractual reasons. I specifically went to this company because of its history with Denon, but when I got there I couldn't find any and asked. Apparently Denon didn't like its products being sold with so many other competing models (in this highly successful. large volume company).
While there has been much talk about how the Onkyo receiver has some 'cheap' amps in them, I do also know that its output wattage is higher than the Denon's (100w vs 90w - and in some cases can spike up to 115w). I have my Onkyo pushing a 7.1 MartinLogan setup and I have been very impressed.
The Denon 'CI' line does carry a 3-year warranty vs 2-year for the Onkyo, if that is a concern for you.
I don't think you can go wrong with either, and the odds out there would put the Denon way above for reliability and potentially no-issues vs the Onkyo, but again...I am very happy with the NR616 and glad I purchased it.