You have to qualify and grade for the right transistor; it depends on the manufacturer and process. Not all 2N3904s are created equal.
The collector-base junctions are pretty slow but high voltage low leakage diodes are slow as well which the BAV199 datasheet shows. When used for an input protection circuit, this does not matter unless you also want fast recovery from overload.
The good emitter-base junctions I tested had about equally low reverse leakage compared to the collector-base junctions in the picoamp to 10s of picoamp range but of course the reverse voltage is low. The good ones had a recovery time which was close to my best reference level pulse generator at about 600ps. The fast low leakage but low voltage diode I was thinking of was used as a clamp in the z-axis amplifier in a Tektronix oscilloscope and was rated at I think 600ps, 15 volts, and 50pA. I wonder if I can find it going by memory since I did not keep my written notes ...
Tektronix 465 - CR1464 - 152-0153-00 - 15V 50mA - Fairchild Semiconductor FD7003,PG7026,TID777
Well, I was close. 15 volts maximum but 10 volts working, 100nA (not low leakage but I think that is the maximum specification), and 750ps which is the fastest silicon diode Tektronix listed a reverse recovery time for.
Next time I will get some photographs of my results but I am holding off until I have a faster pulse generator and I want to use a faster oscilloscope.