Well,you're gonna have to provide a few more details. How are you receiving the video file? If via MMS, that's probably why you're seeing the reduction in quality as MMS doesn't support high-quality video and instead, compresses it to send a MUCH smaller file. If you're using direct file sharing like Bluetooth or apps like PushBullet, the video should be without quality loss (unless, of course, the original video IS of low quality). When using IM apps like Facebook Messenger or Whatsapp, the level of compression when sending videos usually depends on the app, but you can expect it to be compressed.
The thing with iPhones is that, when sending messages between iPhones, they use iMessage, so whatever they send is usually not so compressed (as if you were using, for instance, Whatsapp). But when sending to another phone, it switches to SMS/MMS but doesn't tell the user that, so for them, they're just sending the message 'as they always have done', but you're not receiving it properly.