Assuming that these are the same classes done at the DFW HamCom, the Basic class has the basic information you need to identify severe weather (pretty much Skywarn 101) while the advanced class gives more details on how to predict when severe weather may develop (pretty much Skywarn 201). Hamcom also had a class called "Interpretation of Weather Radar Imagery" which gave information on how to understand the radar images in much more detail than the basic "my area's green so it must be raining and a red spot is heading my way so it will probably rain harder soon".
For some areas like the DFW area, the basic class is just that, the basic (minimum) information you need to be an effective storm spotter while the advanced class provides additional details that provide additional detail that was only summarized in the basic class as well as provides additional information into how a storm forms and becomes severe. The advanced class also touches on understanding and interpreting the weather balloon information available on the NWS web sites.
Other areas do things a bit differently though. Their basic class is shorter (2 - 4 hours long) and has the basic information (pretty much like the DFW basic class). Their advanced class is longer (4 - 8 hours long) and includes both the basic and advanced class information, but in a single class. The additional information in this format is provided right then instead of them saying "the advanced class discusses this in more detail".