Advantages: If you are NOT pushing past the exhaust backpressure limits, then you have no wastegate to bleed off exhaust and you won't loose boost.
Disadvanages: If you ARE pushing past the exhaust backpressure limits, then you risk damage to your turbo.
A wastegate is designed as a "safety" release. Smaller turbine housings need a wastegate to bleed off excess exhaust pressures to keep from creating too much of an imbalance with the compressor side. For example, if you disable the wastegate on the stock turbo, and routinely push it well beyond 25 lbs of boost, you will most likely kill the turbo in a very short amount of time.