CJ,
ADS Advantages are lots of examples and templates to get started, and disadvantage is difficulty of using the software. From a simulation perspective no real advantages as it is mature (i.e. old) technology.
AWR is more modern software and more intuitive and easy to use. Advantage is in the linear models (microstrip, stripline, CPW), but this is only apparent above 15 Ghz. AWR has both EM based models and closed for m like ADS.
For layout, ADS has old style back annotation engine with layout being a seperate program from schematic. Most people do not like ADS layout and use for simulation with Mentor (PCB) or Cadence (IC) as the real layout tool.
AWR has a unified database (UDB), which means the schematic and layout are always synchronized and work from very same database. If you change one the other view "mirrors" the change instantaneously. It is a different paradigm and it works well once you get used to it. This approach is best for mm-wave and MMIC, but can be cumbersome on huge circuits (i.e. more than 1000 densely packed models in RFIC or PCB).