Sonata Form Theme Groups

Hi,
I was wondering about sonata form. In a classical period style sonata in a major key, two different theme groups found in the exposition are usually in the tonic (group A) and dominant key (group B) of the piece.

In general, how do these different theme groups A and B differ from one another? (With regards to melodic content, liveliness, dynamics, etc.)  And, conversely, should they share any characteristics or motives?

If you're interested, I'm wondering what sort of group B to follow the first half of the exposition in this piece:

http://www.youngcomposers.com/music/listen/6083/woodwind-trio-in-eb/

Any help, suggestions or insight would be greatly appreciated!

When it comes to the relationship between the main theme and any other theme(s) there's no real right or wrong way. Beethoven's 5th piano concerto 1st movement's second theme has no thematic relationship to the main theme. Then there is a piece like Brahms' 4th symphony where almost all the themes are related. The only thing that seems to be consistent is that a new theme tends to offer contrast to the main theme but also keeps in character with the rest of the movement. But even then I'm sure there are exceptions to that as well. Again, there is simply no one way or right of going about it. 

When it comes to the relationship between the main theme and any other theme(s) there's no real right or wrong way. Beethoven's 5th piano concerto 1st movement's second theme has no thematic relationship to the main theme. Then there is a piece like Brahms' 4th symphony where almost all the themes are related. The only thing that seems to be consistent is that a new theme tends to offer contrast to the main theme but also keeps in character with the rest of the movement. But even then I'm sure there are exceptions to that as well. Again, there is simply no one way or right of going about it. 

Thanks for the answer!

I've just completed a first draft and hope the two theme groups work well together.

how do these different theme groups A and B differ from one another?

Short answer: they should contrast with each other. The ways they contrast are different from piece to piece, but character/affect are especially relevant in CPE works.