It seems both protocol does the same thing but is there a advantage of one over the other?
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/