Container names do not identify every codec
MP4 and WebM are containers that can hold audio and video encoded with particular codecs. An MP4 file does not reveal every stream property from its extension alone. Check the source and target requirements for video codec, audio codec, resolution, and profile.
A conversion may re-encode the streams rather than simply changing a wrapper. If the source is already compressed, a new encode can alter detail. Keep the original MP4 and compare representative motion, edges, and sound before using the WebM as the only delivery copy.