These areas should give you most of the general differences and similarities you are seeking; asking for an explanation of everything is a bit too broad for people to answer easily or quickly on the forums.
Happy reading!
One thing to note is that the Homework Board can only be powered by a 9 volt battery. The Activity Board has a regular DC input jack and can also use USB for power.
Comments
Basically, the Activity board is Propeller based. Programmed with Spin, PASM, or C.
Homework Board is BS2 based, programmable with Basic Stamp Tool only.
Propeller has many more I/O pins, (up to 32, but conservatively 28), runs much faster, and has 8 cogs .
We try very hard to provide that kind of information on our product pages and on the Learn site if we can.
I suggest looking at the following product pages and their product guide downloads:
http://www.parallax.com/product/555-28188
http://www.parallax.com/product/32910
As well as this page from our brand new Teach section on Learn:
http://learn.parallax.com/teach/microcontroller-education-board-options
These areas should give you most of the general differences and similarities you are seeking; asking for an explanation of everything is a bit too broad for people to answer easily or quickly on the forums.
Happy reading!