Fundamentally, there is a huge difference in the expenses for both procedures.
Annulment of a church marriage is more expensive than annulling a civil marriage since there are additional procedures to follow for the church marriage. If you desire to have another church wedding, mere civil annulment through a final order of a court will not automatically apply as per the Church because the church procedures are dependent upon canon law. Hence, you need to have a canon lawyer represent you in front of a tribunal composed by priests who are authorized to handle annulment cases. Such procedures make the annulment of church marriage longer and more tedious.
In civil marriage annulment, the mere declaration of a court that the annulment is granted upon final order is enough to dissolve the marriage and both ex-husband and wife can remarry again upon proper procedural filings. Therefore, the shorter period presupposes a cheaper overall expense when compared to the church procedures.
It is important to note that if a civil case for annulment has been granted in your favor, you can remarry again in civil rites BUT not in church rites if the church procedures weren't followed.