You guys are getting lost in numbers a bit.
Comparing titanium to steel is apples and oranges. And a misnomer in both cases.
Titanium can not match the strength of steel, not the hardness of steel. But titanium exceeds steel in some other forms of material performance. I am a knife collector and we discuss this sort of thing in great depth, with knife makers and even material physicists.
Many high end knives are made with a titanium alloy handle and a good steel alloy blade. Like a Chris Reeve Sebenza for example. Each of these has a titanium handle and an S30V steel blade. They run around $450-500 a piece, the plain one around $375-$400.
Most titanium, though it is one of the most plentiful elements on earth, is not pure titanium, so there is no one such thing as "titanium", you have to be more specific. Much of what is called "titanium" is alloyed with other materials, usually aluminum and platinum. This matters as to the material performance. So when discussing the material you have to be specific to the exact alloy of the titanium, it's very rarely pure titanium crystal and that substacne is not very useful. Titanium is expensive because of the process needed to separate it from the ore(most commonly the Kroll process
if you are curious, there are other means but Kroll is far and away the most common for now), but the titanium itself is everywhere on earth, very plentiful.
Nor is there one "steel", you have to be far more specific. In fact many steels used today are alloyed with forms of platinum, and aluminum, and many other material elements. This makes modern steel very uniform in molecular and carbide structure, and able to reach hardness levels thought impossible only 10-20 years ago.
You take a ZDP189 steel? A Cowry X or Cowry Y steel? These are some of the most amazing alloys on the planet. S30V, S60V are two other 'high end' steels. Then there is good old CPM154 designed for jet aircraft engines, this is one of the most common higher-end knife steels today, or the Hitachi equivalent of ATS34. A2, D2, 1085, 1095, 52/100(great stuff), 12C27, AUS6, AUS 8, VG10, SGPS, etc... many, many steels.
The way a steel performs depends primarily on the way it is heat treated, this is even more important than the recipe(mixture of elements). The heat treatment of metals is the oldest and most explored form of material physics in the history of man, it literally changes the molecular matrix and the nature of the molecules themselves. So you can't make strength or performance judgements even based on the recipe(type) of steel alone either. How was it heat treated? with what Rockwell hardness in mind? Titanium is even alloyed into steels.
There is no simple answer to this question except:
In strength of any type including tensile, and hardness, steel wins by a long shot.
In resistance to temperature(very high melt point give titanium a high ceiling of 'temper') tolerance of vibration, certain types of torsion stress, strength to weight, and corrosion resistance, titanium wins.