MOV is Apple's container and it is fine until it is not. The real question is browser or desktop.
- Online wins on convenience: no install, done in minutes for small files. - Online loses on everything else: upload times for big files, quality settings you cannot touch, and your footage on a stranger's server. - Desktop wins on control: HandBrake, VLC, Shutter Encoder, free, batch jobs, exact settings. - My rule: under 100MB and non-sensitive, online is fine. Anything bigger or anything you would not want leaked, desktop every time.
Keep the original MOV until you have verified the MP4 plays everywhere you need it. Thirty seconds, saves you more than once. And if you are converting because you want clips for social, ReelCut skips the whole dance and delivers finished shorts for $4.99 a video.