Answer: In most cases where there is a severe erosion problem, two things need to be done. One is to control and direct the surface runoff better, the other is to plant the slope or otherwise stabilize it. In some cases, a mixture of plants is suggested because this will provide a variety of types and depths of plant roots and this is better for holding the soil in place. In other cases, a mass planting of just one plant is adequate. I would strongly suggest you consult with a professional who has training in drainage and grading to determine the best way to handle the water to reduce the erosion before you plant. If the problem is severe enough, it will preculde the establishment of plants, by washing them away and/or leaving an impoverished soil or an impossibly steep situation.
With regard to the plants you mentioned however, bishops weed (Aegopodium) is an invasive plant and spreads by both underground runners and by seed and is nearly impossible to eradicate once established in an area. It also spreads very quickly -- often beyond the original planting area. During the summer it may brown and possibly appear to die back in a hot sunny location if the soil is dry. I would never recommend planting it. Crown vetch is often used by highway departments along the side of the road. It is a rank grower poorly suited to residential landscaping. Neither of these are evergreen.
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