The first thing worth clearing up: titanium and stainless versions of the same part cover the same cars. Same chassis codes, same body styles, same mounting points, same route. Material does not change what the part bolts to.
Weight, sound character, corrosion behaviour, repairability and price. A titanium part of the same dimensions weighs roughly 40 to 45 percent less than its steel equivalent, which matters most when that weight sits ahead of the front axle or high in the car. Titanium also produces a higher-pitched, more metallic note than stainless in the same design.
Cost, and forgiveness. Stainless is easier to repair and easier to modify if you decide to change the system later. For a car that sees road salt, track abuse or regular welding work, that practicality is worth more than the weight saving.
Weight and heat. Titanium is a poor conductor of heat relative to aluminium, so a titanium intake path rejects far more of the radiant heat from a turbo and manifold than an aluminium one does. Combined with the weight saving, that is why it is the material of choice on high-output turbocharged cars.
Ask three questions: how much does the weight saving matter on this car, how much does the sound matter to you, and how likely is this part to be modified or repaired. The answers point one way. You can compare both materials across the Titanium Exhaust System and Stainless Steel Exhaust System ranges.