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Both are equally important.
Knowing Manufacturing process shall help you to design in cost effective way with optimized processes.
A Design Engineer need to know quality requirements & processes too ensure that right parameters are controlled in his designs. Right quality is best for all products. Neither over quality nor under quality is accepted in Companies.
The experience of manufacturing/quality control will be useful in design field if the product is same. For example, you have experience in manufacturing of autombile parts, so any company dealing in design of automobile parts will definitely consider you for their design engg department.