What are the pros and cons when using a Workflow Rule Field Update vs. a Formula Field?

Hi Manpreet

First thing to remember is that "Worflow rule" is not a field type in salesforce. Workflow rule is the process automation tool that automate your business flow .
Formula field: it is a field type on salesforce that produce a read only ouptut. Sometimes u want some calculated value in a field lest say i want my total sell in day in one field then i can create one formula field on my object and i will write a formula that will calculate total sell .
The field included in formula field is called it's source.

Now there is a similarity between workflow and formula field.:
Whenever there is a change in the source field of formula field it automatically re-calculate its field value according to updated value in the source field.
In same fashion workflow can also do the field update.

one more thing formula field can't use the workflow but inside a workflow we use formula field.
there are only one criteria to update the value of formula field but for workflow u can define different kind of criteria.

Hope it will help you.