Generally, larger particles decay more slowly and cause less nitrogen depletion. If the bark mulch sits on the surface and is not worked into the soil, there should be minimal nitrogen depletion. Of the three mulches you listed, cypress is especially slow at decaying, which somewhat offsets its higher cost. Pine bark (called nuggets) sometimes floats away and is susceptible to erosion. Because most bark mulches contain large particles, they can be applied to a somewhat greater depth than other mulches, as much as 4 to 5 inches deep. Also, there is some light penetration, which means weeds may germinate. You can counter this by applying bark mulches over landscape fabric.
With all wood mulches, be aware that improperly stored or handled wood chips or bark can lead to "sour mulch." A good discussion of sour mulch, including how to recognize it, can be found at this
Virginia Tech Web site.
Before mulching, it would be a good idea to get a soil test to address your perennials' nutrient needs before you put down the mulch. Contact your local Extension office for instructions.
A good discussion of various mulches can be found in this
Yard and Garden Brief.
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