The advantages of holding a physical certificate include:
The company knows how to reach you and will send all company reports and other information to you directly.
You may find it easier to pledge your securities as collateral for a loan if you hold the certificates yourself in physical certificate form.
I would add that if the investor holds the certificates, they are not able to to be shorted because they are out of the system and can't be borrowed against....legally. (General statement about all stocks)
The disadvantages include:
When you want to sell your stock, you will have to send the certificate to your broker or the company's transfer agent to execute the sale. This may make it harder for you to sell quickly.
If you lose your certificate, you may be charged a fee for a replacement certificate.
If you move, you will have to contact the company with your change of address so that you do not miss any important mailings.