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From your question I will assume you are asking about top load washers. Front load washers do not use wash plates or agitators.
Top load washers that use wash plates are the water conserving types. They use less water and are more environmentally "friendly". These washers require the use of a quality high efficiency soap to properly and completely clean clothing. No agitator means a bigger basket that holds more clothes. The wash plate gives a gentler wash that can be used for a wide variety of fabrics, while agitators are more damaging to your clothing.
In my opinion the wash plate is a better choice.
Here is a link that you may use to view the different choices you have;
Top Load Washers