What Kind of Retainer After Braces is Better, Clear Plastic or Wire?

Ultimately, compliance is the key.  Clear trays allow usage at all times of the day, wires tend to be worn only at night.  Nothing works 100% of the time and you will hear arguements for each style.  Wires do allow some modification that clear aligners do not.

There is no right answer.

All retainers are effective, wire retainers are more durable, clear retainers are more cosmetic and fixed retainers are permanently cemented behind the teeth. It is easily possible to add springs to the wired retainer to realign the teeth that have moved.

The choice for retainers are determined case by case... In my office there few cases where I recommend the metal retainers (Hawley), but majority of the time I recommend clear retainers... 

Both, plastic and wire retainers work. Plastic retainers, also called Essex, are great, but it is recommended to change them every 5-6 month, because plastic becomes less retentive over time. Vivera retainer is another brand of the same design.
Wire retainers, also known as Hawley retainer, should be periodically checked by a dentist and adjusted, if needed.
There is also a  fixed wire retainer called Lingual Bar, which is attached to the back side of the lower front teeth. It is invisible when you smile and hold the teeth the best.
There are several options when it comes to retainers. All have pluses and minuses. You can pickup option that works for you.

                Both types of retainers work well as long as you wear them correctly. I would return to your Orthodontist to determine how much relapse of your teeth has occurred and together you can decide on the proper retainer for the problem that you had. Be honest and let them know how much you are willing to wear the retainer. Good luck.