There are probably more disadvantages of dating someone older than you compared to someone younger than you. Depending on how old you are and how old the other person is, you may experience some disadvantages.
These include that this person may have trouble keeping up with you. You may enjoy certain athletic activities and they are too old to do the activities with you. You may feel that you have to sit around with them.
Also, they may experience more medical problems and you have to be willing to nurse them back to health even though you are completely healthy yourself. This all depends on the age difference. If your significant other is a lot older than you, you may experience more disadvantages.