I notice that on my iPhone, when I use my personal hot-spot to distribute Wi-Fi, if I have Bluetooth enabled, the phone will make a Bluetooth connection to my laptop instead of a Wi-Fi connection.
So I'm wondering:
Is Bluetooth faster than Wi-Fi?
The Bluetooth standard maximum data rate is at best 3Mbps or about 2.1 after protocol overheads take their cut.
Wi-Fi on the other hand maxes anywhere from 54 to 1300+Mbps depending on whether you have "g", "n", or "ac" Wi-Fi and what enhancements the adaptors and router support.
So no. Bluetooth is not faster than Wi-Fi. Not even vaguely close.
Bluetooth v3 and v4 have higher data rates but the actual data transfer in those implementations happens over Wi-Fi; Bluetooth is only used to set up and negotiate the connection.
For the purpose of tethering a notebook to the internet via a mobile phone in the field, the most important difference is power consumption and range.
The Wifi tether can consume your smartphone's battery in an hour, while with the Bluetooth tether you can go for hours, and the phone will not shut itself down before the notebook does.
So what can each kind do and not do, besides the power requirement difference?
So when to use which one? From the above it should be obvious: