The thing for me that is so gripping and fascinating about Titanic is the role which coincidence plays in the tragedy. It is a virtual tapestry of errors, and with any one thread removed from that tapestry the tragedy either doesn't happen at all or is greatly diminished. Compounding the string of human errors are such added coincidences as the novel Futility and its fictional ship Titan, and all the hype surrounding Titanic before the voyage.
Titanic is a tragedy that should never have happened -- the odds against that many things going wrong are surely incalculable. Had it been a work of fiction it would have been dismissed as totally implausible because chance plays too great a role in its happening at all.
Another element of interest for Titanic that Lusitania lacks is the length of time the two ships took to sink. Lusitania went down in 18 minutes versus 2 1/2 hours for Titanic. Those 2 1/2 hours really gave the Titanic tragedy time to breathe and deepen in its impact, allowing all on board to contemplate what was happening and to make choices that continue to fascinate us all. The level of drama, heroism, and human interest I think is higher here because of the amount of time involved. The story of each life saved or lost becomes that much more poignant because there is time to reflect on the situation while it is happening.
The Lusitania tragedy was almost inevitable. Passengers were warned in newspaper ads placed by the German government that ships flying a British flag were liable to destruction. Lusitania was hunted down and destroyed intentionally, but the iceberg never took aim at Titanic -- it just happened. The two are such different kinds of tragedy, but the element of chance in Titanic is for me the thing that elevates fact into the realm of myth.
If Titanic is the number one shipwreck story of all time, though, Lusitania is likely number two, and I would suggest that
Andrea Doria is number three, in a story where human error actually approaches Titanic in terms of the cause of the tragedy but where the loss of life was thankfully greatly diminished from 1912.