Tungsten is more dense and harder than lead. This will cut your size of weight roughly in half. The smaller size in most cases will help to alleviate a lot of hang ups as well as give your bait a more realistic presentation. Given it's properties it transmits sound and vibration better than lead and the added vibration transition will allow you to have a better feel of the bottom. Also, because it's harder, it won't deform like lead. Believe it or not, because lead is such a soft metal, a basses "teeth" or Velcro-like ridge can actually dig into lead when you set the hook reducing your hook setting power. Tungsten's hardness and decreased size will not allow this to happen and effectively the weight slides right through letting you transfer all the energy to the hook set. Above all else, even though using lead weights hasn't been proven to be detrimental to waters, but there's something that tells me that dumping a substance that is known to cause birth defects among other things into our waters can't be a good thing. Tungsten although more expensive is a more environmentally friendly material.
There have been reports of people having issues with the insert free weights cutting line, but these are due to poorly made weights. If you're in the market, check out Eco Pro Tungsten. Not only will you have zero issues with them, they also make some very innovative products that you won't find anywhere else!