Why are most IR phototransistors slow?
Photodiode + transimpedance amplifier can give you much faster response. Quite a bit of good information has been written. Anything by Phil Hobbs will be useful. 

By keeping a constant bias voltage across the PD you can reduce the effect of the diode capacitance. A constant and large reverse bias will further reduce the capacitance. 

More light will allow you to use a smaller (lower capacitance) PD and lower value feedback resistor, so you'll get faster response. 



A phototransistor is like a PD between the collector and base of a transistor so you get the PD capacitance multiplied by the Miller effect. If you bias a phototransistor so Vce does not change you can get faster response out of it.