For proj.4 those two mean exactly the same and conversion from one system to another changes only the EPSG code. If you work with geodetic problems which require accurate ellipsoid model you will need some other tools.
# ETRS89 <4258> +proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs <> # WGS 84 <4326> +proj=longlat +datum=WGS84 +no_defs <>
The difference is rather small as written in the documentation of another conversion tool
Please note that the GRS80 and WGS84 are considered to be the same. Actually, there is a very small difference in the flattening which results in the semi-minor axis, b, being different by 0.0001 meters. There is no known application for which this difference is significant.