I use both Fuji Pro800Z and Portra 800, though mostly Portra 800 (the current 2006 version) because I find that it has a slight edge in terms of higher effective speed in tungsten light and lower graininess. It is also more pushable - I'm happy pushing it two stops (I don't bother with a one stop push for colour neg film) and rating it at EI 2000 in tungsten light. I don't like to rate pushed Pro 800Z that high - I'm more comfortable with it at 1250 or 1600.
One thing that has just become clearer to me is that Portra 800 has better spectral sensitivity in tungsten light than Pro 800Z.
You should be able to balance up both Portra 800 and Pro 800Z when printing after shooting it under tungsten-ish lighting. With both films (or any daylight neg film used in tungsten lighting), the more exposure you give them, the better you will be able to balance the shadows. They all have a blip on their graininess graph down at the toe, so that's another reason to keep important detail way from the toe.
Best,
Helen