It's more common to light soundstages with tungsten because (1) they are much cheaper (though they draw more power), (2) they look nice and are more flexible, can be run through a dimmer board, come in wattages down to 100w and less, etc., (3) you often have night interior scenes anyway that use tungsten lamps, and (4) HMI's are temperamental, not as reliable as tungsten (ballasts overheat, there are flicker issues, hot restrike problems, etc.)
There are some exceptions -- the giant set for "The Terminal" was lit with HMI's because Kaminski wanted to keep the real color temp difference between the daylight and the tungsten used in the food court stalls and stores, etc. The opening scene in "Inglorious Basterds" because it was shot both on location with real daylight plus HMI's and then finished on a soundstage, so Richardson wanted to use the same types of units as he did on location. And I did it for "Manure" because I was using the Red One camera, which looks better in daylight color temps, and it was easier to add a big soft light over the landscape soundstage set using Kino blanket lights, and because I was using Kinos, I could easily use daylight tubes instead of tungsten tubes. This also allowed me to use big tungsten lamps when I wanted to create an orange sunset effect since the camera was set to 5600K.