The pro is that you don''t pay as much, the con is that you pay all of it.
If you claim costs you can agree to share or delete the claim for costs if the respondent cooperates with the proceedings.
If you personally serve the Petition and receive no response, you can forge ahead and get your costs order. However, you still have to enforce the order if the money is not readily paid.
So, in essence, you can use the claim for costs as a bargaining tool. If you are acting in person, your costs will be limited to the court fees of £385 and the process server if you have to use one which might be £250 or more depending upon which country the respondent is in.