I was just reading this article on how Curiosity's aluminum wheels are getting pretty dinged up. Usually titanium alloy is considered an upgrade from aluminum alloys in most applications, from aerospace to bikes to sporks. The "usual" downsides are that it is expensive and difficult to machine. However, those seem like less important factors when you're NASA and the plan is to send an object to another planet and drive over sharp rocks.
This answer from Reddit indicates there were two drivers, minimizing mass of the wheels for part of the landing sequence and expense. Expense is a tricky one because they wanted a very strong starting material. That limited them to block or extrusions. They could find aluminum pipe extrusion stock, but not titanium, so ultimately that pushed them to aluminum. Since they were machining the wheels down from pipe stock, that placed a minimum thickness for the wheel material due to machining tolerance, so even if they had a titanium source that was cheap enough, they couldn't make the wheel any thinner to lower the weight to what titanium would allow, so that was the other reason they ended up choosing aluminum. Credit to my coworker Tiffany for the Reddit find, and my coworker Matt for also pointing out that the low temperature on Mars would have also exacerbated the brittleness concerns for titanium.
Aluminum is less dense than titanium. For the same mass, the 0.75mm thick aluminum would have to be replaced with 0.45mm thick titanium. Although the titanium sheet would be stronger in tension, it would probably be more susceptible to tearing from a point load like driving over a sharp rock.