ANT/ANT+ is a proprietary but open access multicast wireless sensor network technology. It's data rate and the resulting application throughput of 20 to 60 kBit/s is significantly reduced compared to its competitors, i.e. Bluetooth and ZigBee. For applications that get along with that restriction and a physical range that is comparable to other wireless network systems it might well be an interesting alternative. It would seem that it is primarily used by sports and fitness sensors by a number of manufacturers.
This Wikipedia page states that:
Geräte benötigen beim Empfang oder Senden weniger als 50 mW Leistung. Da sie die meiste Zeit im Sleep-Mode verharren, ist die Gesamtstromaufnahme gering.
Which roughly translates to:
Devices require less than 50 mW of power when receiving or transmitting. Since they remain in sleep mode for most of the time, the total current consumption is low.
It focuses on ANT being specifically well suited for low power sensor networks with less than 50 mW of power consumption during transmissions and being in sleep mode most of the time.
However, one would expect any battery powered appliance (and even more so devices powered by energy harvesting) making heavy use of deep sleep modes during times of inactivity. I wonder how a "real life" sensor network using ANT would compete against other technologies such as Bluetooth low energy in terms of power consumption?