It is best to obtain a native species list for your region or physiographic area. Botanists and soil scientists often have a good idea of which plants are suitable. The plants used for erosion control will vary with location, but important to avoid introducing non-native invasive species. Erosion in wet meadow valleys and salt marsh include rushes and sedges, which have deep, dense rooting systems to control bank erosion. If one is trying to stabilize stream banks, it is important to consider bioengineering, which combines some engineering techniques with rapid responding riparian species as black willow (Salix nigra). If given the opportunity, the International Erosion Control Association has annual meetings and technical papers, training sessions, on-line or webinars, etc. that might be helpful. Many plants do not develop rapidly enough, without some added measures, to withstand the velocity and erosive power of moving water. I have seen impressive work of transplanting Vetiver sp. (a hedge species) to help protect fairly high gradient waterways in dam overflow relief channels. In some of our streambank stabilization work, we used live long tree stakes or cuttings of willow, river birch, alder, etc., driven deeply into the soil, or in some instances, bundles of branches buried into the soil. Once on a large river we used a trackhoe to drive in live tree poles cut from larger branches of appropriate species, and this worked too, just avoid putting them where high Public use or fishing occurs, as they tend to cut them off. Sometimes geotechnical materials, mulching, hydromulching or other practices such as stream cross vanes, J-Hooks, barbs or groins or similar practices may be useful to address stream velocity and areas with high near bank stress. The erodibility of the soil or substrate materials may also affect the type of plants or practices used. The USDA NRCS has an Engineering Manual Part 650 that addresses these subjects, and you can probably find it on the internet. The US Corps of Engineers has hydric plant lists including some facultative wetland species that may occur in riparian conditions, and it might suggest some plant types that might also be native to your conditions. If not native species, then consult with botanists to be sure they are not invasive. As you might imagine, invasive species can respond quickly and take over, and may be also good for erosion control, but they can spread and persist elsewhere, possibly damaging to native habitats and species.
In addition to the interesting and comprehensive answer given by William F. Hansen, you can do some experimental works that combine satellite image analysis, DEM, and field work to verify the gradient at the down stream and up stream of different plants. The basic idea is as follows:
1- Use remote sensing images such as Landsat to delineate the boundaries of different plants. For this task you can use and GIS software.
2- Use the regional DEM such as STRM to conceive an idea about the slope or the gradient at the up stream and down stream of different plants polygons.
3- Then do field work by doing precise differential leveling at the down stream and up stream to generate 3D profile.
4- Then compare the different 3D profiles and look for the changes in gradients. This comparison should reveal some critical information about the different rate of erosion.
FYI — Link to Table of Contents NRCS ENGINEERING HANDBOOK Part 650. It includes info on downloads. The complete handbook is quite large, so probably best to select areas of interest.