Using my home-brew pulser, I can resolve a pulse down to around 700ps, which seems to tally with the BW of my unlocked (MSO5104 -> MSO5354) 'scope which is ca. 600MHz.
The response curve of my 'scope is below, and the roll-off post -3dB point is ca. 55dB/decade, which if I am not talking nonsense is almost 3rd order, which means we should expect Rise Time to be 0.45/freq