There is possibly some confusion here but I need to clarify that Quartz bulbs ARE tungsten filament bulbs as well (both "incandescent" bulbs - https://en.wikipedia.org/wiki/Incandescent_light_bulb)
"Normal" bulbs (Thank you Mr Edison), which is probably what you are referring as "tungsten", are filled with an inert gas and are not able to burn as brightly as Halogen Quartz bulbs due to the way the gas inside reacts with the filament (filament evaporation)
Hence Halogen Quartz Tungsten bulbs are capable of much higher output for their size and can take a much higher current.
-> Normal Tungsten filament bulbs have a warm light and are very inefficient.
-> Halogen Quartz Tungsten bulbs burn much hotter and so have a higher colour temperature, ironically called "Cooler"! They also have a significantly higher luminous efficiency (Lumens per watt)
TECHNICALLY they are interchangeable. But are packaged differently, so you would not be able to change between them in a lighting fixture (easily) - A Halogen bulb could also draw too high of a current for the equipment if it was designed for normal bulbs.
As for colour output, Tungsten bulbs are still regarded as one of the best sources available as they have a near 100% spectral coverage, as do Halogen bulbs.
However as they burn hotter / brighter, they also have a significantly more pronounced output in the middle of the spectrum (green/yellow)
Of course it goes without saying that you shouldn't mix sources, just as you wouldn't want to mix natural and incandescent.