Which is better: Synthetic underlayment or traditional felt underlayment?  Bottom line: Underlayment is a vapor barrier. 

Synthetic underlayments are a good product, but the advantage is primarily to the installer:

• Synthetics are lighter in weight, so a 1000 sq ft roll weighs about what a roll of standard 15lb 400 sq ft asphalt-saturated felt weighs.
• Organic (traditional) felt underlayments will 'breathe' whereas synthetics will not. Many roofers prefer 'felt' for this reason.
• Synthetics will not wrinkle overnight like felt will, so the roofer does not need to slice the felt the next day to flatten it out, which saves a little time. Note: If the felt receives 15 minutes of sunlight, it will flatten out. If the roofer covers the felt with a tarp at the end of the workday, it will remain flat overnight.
• Synthetics cost more money than standard felt. Of course that cost is passed to you but the roofer has one less time-consuming issue to deal with (time is money) so the profit margin can be higher with synthetic underlayment rather than with felt.

Simply stated, synthetics are more expensive than felt, lighter, and can be quicker and easier for the installer to use. Traditional felt is less expensive than synthetic underlayment, is a little more sensitive to the elements though it can be easily managed with a little extra care.