There are a handful of Android phones which use the same chip for WiFi and BLE. As a result, you will frequently lose connectivity to WiFi and have to rely on the internet connection you get through your carrier.
We have been compiling a list of phones which we know have this issue and which we know do not.
The following phones are known to be problematic: Nexus 4, Nexus 7 (2013 Edition), Moto X, and Moto G
The following phones are known to work fine: Nexus 5, Samsung Galaxy S3, Samsung Galaxy S4, Samsung Galaxy S5, and Toshiba AT7-C
Please feel free to submit your phones to firstname.lastname@example.org so we can continue building a comprehensive list.