Short answer
MP4 has broad device support while WebM is designed for efficient browser delivery.
What to check
Review codecs, browser support, transparency, quality, and file size. Check video and audio codecs, duration, frame rate, resolution, aspect ratio, subtitles, and audio synchronization after conversion.
Using mp4.now
Use the MP4 TO WEBM converter, keep the source, and inspect the downloaded result before sharing it.