Chromium v.s titanium alloy, which metal is tougher?

As pure elemental materials, Chromium is stronger and harder.

However, both are normally used in alloy form to give optimum properties.

With titanium, an alloy with a few percent other metals included can be many times stronger and tougher that the pure metal.

Chromium, by comparison, is used as an alloy ingredient with other bulk metals to improve their properties rather than being used as the main part of alloys.

The strongest & hardest steel grades contain some chrome, also Nickel-Chrome alloys have extreme properties - eg. Nichrome for such as heating elements & Inconel for jet engine components.

It's main uses in pure or near-pure form are as surface finishes or as wear protection due to its hardness and stability.

I think the application is a big variable in the answer.For a structural item for a spacecraft, the titanium alloy is the one for the job. For a shaft in an industrial machine, a heat treated steel shaft with hard chrome plating will be tougher and wear resistant than titanium would be.