The Third Option
As with many things, there are often more than two ways to do something. The third option in this debate is to combine both options and pay your child a weekly base allowance that will not change regardless of what chores are done. Additionally, have a list of chores that are required to be done always (regardless of what allowance is given). Then, have a list of supplemental chores that are optional and that you will provide monetary compensation for.
Here is an example: Your child is ten years old and receives a weekly allowance of $7. Additionally, he is required to contribute to the family by keeping his room clean, doing the dishes, walking the dog, and taking out the trash. He is not paid for these chores, since they are part of his normal responsibilities, just like homework or showering. However, if he wants to make extra money, he has a list of chores that he can do as well. Examples include: doing the family's laundry ($2), vacuuming the house ($1), raking the leaves ($2), or washing windows ($1).
Ultimately, the choice is yours and you need to find the solution that best fits your family situation.