Tungsten is nearly twice as dense as lead making worm weights about 50% smaller than the equivalent weight lead sinker. This makes them more weedless and easier to fish. The increased density provides greater sensitivity so you feel the bottom and bite even better than before.
Most of the weights are 97% pure Tungsten and super tough to avoid any chipping that could fray your line. Lead weights are cheaper and a small number of birds are harmed by their ingestion. This is not, by any means, damaging to the bird population so should not be a considered concern. The smaller size of Tungsten helps you make longer, more accurate casts and emits a loud ticking sound when banging off rocks. All the Bass pros have moved to Tungsten worm weights. I see no reason not to give myself this advantage since I only get to go fishing a limited number of days a year.