I spotted the Google Map APIs for a while. In my opinion, as a web developer in Taiwan, I might choose Google Map as my tool. I don't mean Google Map is better than ArcWeb Services. In fact, Google Map offer just basic mapping APIs and can't compare with ESRI ArcWeb. But ESRI ArcWeb Services offers little content outside US. We can't get detailed sattlelite images of Taiwan from ArcWeb. Google Map and Google Earth really have very detailed images of urban areas in Taiwan.
But, Google Map has no road map in Taiwan, although ArcWeb has only outdated large scale road map. The best choice is to have your own ArcGIS Server and purchase your own data, it might cost tens thousands US dollars. If you are looking for free services, there are always trade-offs.
For information about ArcWeb Services, http://www.esri.com/software/arcwebservices/index.html
For information about Google Map API: http://www.google.com/apis/maps/