It seems both protocol does the same thing but is there a advantage of one over the other?
The short answer to whether MPEG-DASH or HLS can deliver better quality is simple: there's not much difference between the two. MPEG-DASH used to hold the advantage, but this is no longer the case. By being codec agnostic, MPEG-DASH could deliver better quality at lower bitrates. However, now HLS supports HEVC/H.
Streaming protocols such as HLS (HTTP Live Streaming) and MPEG-DASH (Dynamic Adaptive Streaming over HTTP) are two of the most popular video streaming protocols for transferring video over the Internet today.
Also used by very large platforms such as Youtube or Netflix, DASH is quite similar to HLS in its general structure: sequenced files listed in a file posing as a playlist.
You should ask yourself what is important to you (encoding, encryption methods, standardization, etc.)
Jason Schneid wrote an excellent comparison: http://www.internetvideoarchive.com/IVA/news/2012/09/13/progressive-download-vs.-adaptive-bitrate-how-to-choose-the-format-right-for-you
Here's a quick comparison for Aquary. Too long for an inline reply...
Web Standards: Of the two adaptive streaming protocols MPEG-DASH has the best chance of becoming the unifying standard.
Support: HLS, being older and with Apple pushing hard behind it, has more defacto support especially in older browsers/os/devices. You can support HLS on windows machine by using the jwplayer.
Performance: Not sure but the makers of bitdash, an mpeg-dash player, make this claim: "streaming performance is 53% higher compared to Microsoft Smooth Streaming and 101% higher than Apple HLS".
Conclusion: HLS now, MPEG-DASH tomorrow (and now if you can manage it). The following article is a good assessment of the fractured state of streaming technologies today: http://blogs.imediaconnection.com/blog/2012/04/27/mpeg-dash-its-time-for-apple-to-put-up-or-shut-up/
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