In general, small signals refer to signals where the peak-peak voltage of the signals are a few hundred millivolts or less. Large signals typically mean very large peak-peak signals, maybe even near rail-rail or at least approaching maximum available swing. The factors that affect the bandwidth are different in most circuits under these two conditions. For small signals, the circuits are generally operating in their linear region, and thus the frequency response is due to gain-bandwidth products, node impedances, etc. For large signals, many times there are active devices that are turning on and off, or even going from cutoff to saturation. Thus, the frequency response will be limited by things like slew rate, recovery times, etc.
I don't know if any "hard and fast" rules though governing what is considered large or small signals.