Bluetooth vs Wifi. Which one has more bandwidth?

Bluetooth is a low energy standard designed for short distances suitable to devices that don't require much bandwidth. It is considered a personal area network.

Wifi is developed as a larger scale network allowing greater distances and speeds.

You can see a comparison of their theoretical maximum speeds on Wikipedia.

Note that the two protocols use the same frequency band which can cause them to interfere with each other. Since wifi's signal is stronger, it will likely have a greater impact on Bluetooth than the other way around.

Furthermore, because most countries regulate which frequencies are available for home use, many other home devices could potentially use these same frequencies as well, causing even more interference.

So if you use wifi at home, even more if it's used close to your Bluetooth devices, using the same protocol on all of them may certainly improve the resulting quality.

As a final note, because of their known limitations and common sources of interference, wireless communications are always less stable than wired coections.