TL; DR - Really you could argue it was both, not really so much one or the other. The northerly course really didn't help matters, but the fact that the bulkheads weren't actually watertight also played a role.

There were several issues that led to the sinking. Some people have suggested that the rivets used were sub-par quality, especially given that subsequent White Star ships used different rivets. However, modern scholars have studied Titanic's rivets and don't find flaw in them. For the time, they were technologically sound.

There is the issue of the watertight bulkheads - which actually weren't watertight. The idea was that if they sprung a leak, the compartments would fill and could stay afloat if four of them were filled. However, the way they were designed, the water spilled over into the abutting compartment. The designers just couldn't conceive that a leisure ship would hit such catastrophic damage as to cause that much flooding. They kind of thought they were being overly cautious.

You mention they set a new course to ensure early arrival. Actually, they followed the same course as planned, but they did speed up. Surprisingly, this was actually a pretty common tactic at the time for northerly waters. You might think with all those iceberg warnings, they'd slow down, but they didn't.

Another problem with those northerly waters (aside from all those icebergs) is a sort of optical illusion that can appear over the cold waters, sort of like the mirage you see in deserts. This optical illusion (I'm sorry, I'm forgetting the proper scientific name for it) could hide the appearance of icebergs until you were practically on top of them. It actually probably would have been better for the Titanic if it had hit the iceberg head-on rather than trying to steer around it; had it hit the iceberg head on, it's likely only a few compartments would have flooded, and they'd just be dead in the water until rescue arrived.

There were several other factors that led to the extreme loss of life, but if your bet is focused on strictly why she sank, I'm sorry but you both have valid points.

For more information, especially about this optical illusion in arctic waters, I suggest viewing the documentary Titanic's Final Flaw.