I don't see how a big ship is more likely to sink. By far more small ships sank than large ones. Titanic was the first large one to sink (by today’s standards at least), but smaller ones had sank due to ice-bergs before.

I am convinced that the reason people think big ones sink is due to the fact, a large one will get more press than a smaller one. I mean a small fishing boat sank off the coast of Norway not long ago, I only know of it because I read it on a linked web site. However if the QM2 where to sink, it would be all over the papers.

Logically a large ship is more likely to hit something, but not more likely to sink, if anything less likely, due to it's many compartments, which are more evident in a large one to a small one.