Html5 tag video VS Youtube video

Both have advantages and disadvantages. As @Evgeniy said, from an SEO perspective, there is no difference. It is the SEO of your page that includes the video, regardless of its source that is important.

When you embed a YouTube video, Google is doing the serving. Your website only needs to output the code for the iframe and YouTube does the rest, so you same on bandwidth by using YouTube. There are also behaviors that come from YouTube, some of which can be adjusted but essentially, YouTube decides how people experience your video, including choosing which version to serve since YouTube creates streams of different resolution to deliver to different devices.

The HTML5 video tag is simpler which gives you more control but also more work, depending on the features you want. Everything comes from the same server, so there are instances when a browser will delay loading the video, compared to an iframe which its src attribute point to a different server. It happens because most browsers have a limit on the number of connections per host, so if there are resources still being loaded from your site, it will wait to load the <video> element, while it would not wait to load the <iframe> since it is hosted by YouTube.

From the "pure" SEO point of view there is no difference between implementation variants you mention. Both of them are equally good or bad recognized by Googlebot as video files.

Much more important is containing of meaningful structured data to describe your video. Because Googlebot can't recognize without structured data about what your videos are.

Also important are the video title, description, categorization in your youtube account, where the implemented video is hosted.

Is it better to embed a Youtube video in an Iframe or to load the video on an HTML5 tag ?

Both tags iframe and video loaded with the download of the current webpage. This can have a negative impact on the speed of downloading the web page, especially for mobile devices and especially in regions that do not have a connection to 4G. We know that Google’s mobile-first index is coming in 2018. Search-result rankings for your desktop site will be based on the signals from the mobile version. The speed of downloading webpages is important for mobile traffic. Mobile users expect to download webpages between 2 and 3 seconds. Download speed will be Google's search rank signal. For an example, try downloading on your smartphone this AMP webpage online of magazine Time with video. Analysis of download speed of this AMP webpage of WebPagetest = more than 15 seconds. This is completely unacceptable for mobile users.

Possible Solution:

• Apply meta link preload (if this web page is not amp - with amp this meta creates a validation error), eg. <link rel="preload" href="your-youtube" as="video" >
• For amp webpages you can apply AMP Cache.
• Also you can apply SMIL.

Which's better from an SEO point of view ?

Set your YouTube as a button.

Eg. <a class= button href=https://www.youtube.com/embed/zzzzzz>My Youtube</a> - replace zzz with your video's id of YouTube - youtube.com/watch?v=XT2kHxSFMS0 - the allocated letters of the link and there are video id.

In this case, the video will be downloaded only when the user clicks on this button. To preload the video you can use any of the meta that proposed W3. For amp webpage see above.

Is there any difference on the loading time, optimization and the maintainance?

See all of the above.