I've heard that the problem with tungsten rings is that if you bash your finger badly and end up in the hospital, it's much harder for them to remove than softer metals like gold or silver. If your finger has swollen due to an injury, they have to cut the ring off, and their tools don't work on tungsten, increasing the risk of amputating a finger that could have otherwise been saved.
So, uh, no thanks on the tungsten. I'll stick with nice, soft, white gold.
Tungsten is actually much easier to remove as it shatters. It also means its safer because it will shatter instead of bending in and cutting off your finger.