HDMI out will work great on both iOS and Android. You'll have the screen perfectly mirrored to the larger TV, while all the exercise tracking is still done on your phone or tablet.
AirPlay will work OK for iOS platforms. On the plus side the AppleTV unit can instantly stream our HD streams and play it full screen - it looks amazing. The downside is that we do not have the ability to do analog speed control, so the tour will either play at normal speed or be paused. Furthermore we cannot composite on trail facts over the video - they must be viewed on the Phone or iPad itself.
Chromecast should solve a lot of the problems with AirPlay. It certainly will be able to stream the tours from the internet in HD, and will also probably be able to give us analog speed control over the playback. We're actively experimenting with our chromecast unit and will report more details when we have them.