It doesn't seem to be very clear to me as to what is free or not out of the Xilinx tools.
There's nothing prohibiting you from downloading both packages and exploring.
For example, Coregen is part of webpack, but which CORES are free and which ones are not?
Standard building blocks like single-/dual-port RAM/ROM, FIFOs, PLLs, etc are instantiable. It goes without saying that what can be generated will vary based on your chosen device.
Also, as to what tools AREN't included in free Xilinx tools, are they useful for the hobbyist?
Most hobbyists will have their hands full grasping core functionality, let alone additional included features. Either suite should be more than sufficient for all but the professional hobbyist.
Is Altera better in that regard?
Off the top of my head, Xilinx no longer offers free Modelsim licenses. Besides that, the question is moot.