just let them sit and become compost or pull them up and compost them?
Depends on the type of plant and why they "died":
Perennials (they grow back next year) - remove dead growth and compost it, leave roots in for next year (some people like to divide the roots in two or more parts and replant to get more new plants next year).
Seasonal bedding plants / annuals: pull them up and compost them
Deciduous shrubs and trees (will refoliate next year) - just remove the foliage that has been shed and compost it
Plants that died due to virus / fungus / pest infections - dig up and burn to minimize the chance of the infection spreading to other plants.
Best wishes - Majikthise.
I wud pull them up and then compost them