Excretion of various wastes and water requirement
Ammonia is more water soluble and also more toxic than either urea or uric acid but it is energetically less expensive. So, in regions where deficiency of water is not a problem, ammonia is an excretory product. Where water is scarce urea or uric acid is the excretory product but it is energetically more expensive to manufacture them. So, you can see an obvious trade off between energy expenditure and water conservation. 

You can refer to any introductory biology book like campbell for further reading.

UPDATE : 

Ammonia    : Most toxic , Easily Soluble , Less Energy Requirement

Urea       :Moderately toxic , Moderately soluble , More energy requirement(As needed to be processed from ammonia

Uric Acid:Least toxic , Least soluble , Highest energy requirement ( As needed to be processed from ammonia )

It is obvious now what tradeoffs are involved.

The only tradeoff not deducible from above is that of the eggs/youngs. In birds, eggs are not permeable for water so the best option is to excrete waste in form of uric acid so that high concentration of waste does not build up. Uric acid is excreted in form of solid palette which can stay in the egg without any harm. 

We can also think of tadpoles which live exclusively in water and so they excrete ammonia but the frogs live both in land and water and so while on land they excrete urea as dessication is the main problem there.