Which option is best male or female? perfect customer service representor for convincing the client to avail your services?

I see that his depends on the nature of the product and the type of the customer. I suggest that you concentrate on the customer who sees value in your product(s)/service(s) rathet than the one interested in the gender of your customer servces rep.

It depends to the kind of service is provided.
Some women customers trust to deal with men.
So many men customers like to deal with women.
The best is to have both genders working.
If one can't satisfy his customer the other one will do.

As far as customer service is concerned,according to me it really does not matter whether you are a male or female.Important in customer service is your attitude towards your job as well as to customer.Another important thing is Listening skills.You can only convince a customer once you listen to him,half listening will not work.Also,your communication skills,your paralinguistic skills,presence of mind and most important is KNOW YOUR CUSTOMER ,that can only happen when you are a good observer .Everyone says FIRST IMPRESSION IS THE LAST IMPRESSION.....but I would say .....U NEVER GET A SECOND CHANCE TO MAKE your FIRST IMPRESSION.........
With your communication skills ,you can actually make the customer think in the same way which you want him to think.If this happen ,success is yours.