Detectors for fiber optic data transmission need a very fast response time. For gigabit data, you need sub-nanosecond response. LEDs are much slower. They're also less sensitive, which means you need a higher-power transmitting LED to get the same range.
That's a rather vague statement, it is the textbook answer directed at the users of discretes: given a fixed discrete photodiode part and a fixed load resistor one can change the capacitance by reverse biasing and thus improve the bandwidth of the resultant RC filter.
But this is not a full truth from the perspective of the photodiode designer: he can trivially increase or decrease the capacitance by designing a photodiode with a larger or smaller area. Suppose ratio of the incoming light power over photodiode area is unaffected by doubling the original photodiode area. If he doubles the area and hence capacitance, then he also doubles the injected photocurrent! Hence he can halve the load resistor, hence the bandwidth is unaffected by doubliing capacitance!
Consider the source illumination, what is the smallest area you can concentrate the light in? If it is smaller than your photodiode's active area, it pays off to select a smaller photodiode since the unused area is contributing dead weight capacitance. But if decreasing the area does not increase the optical power / photodiode area ratio, you need better optics or illumination.
