The purpose of an amplifier is to increase the level of signal from some level of input to a more usable or desired level. Gain factor is just that - The numerical factor defining that rate of increase.
In the audio entertainment realm, that could involve a 150mV signal from a turntable into a 20,000Ω input (1.1µW) being amplified to a 12V level into 8Ω speakers (18W). The basic math indicates that would require an overall power (wattage) gain of around 16 million. That is difficult to do in one stage, so through the various stages of an amplifier that level of multiplication of voltage and current needs to occur to achieve the desired output.
A transistor amplifier is practically limited by the voltage applied to the circuit and current available from that power supply. The early stages of an amplifier, typically used for equalization of input signals, can use relatively high voltage circuits to rapidly increase gain. A typical phono EQ amplifier operating at 30V can amplify that 150mV signal up to the practical operating limits of the transistor before distortion is introduced, and most often a safety factor is applied to designs so that peak inputs do not exceed those limits. In our example, that 150mV signal (7.5µA) applied to the base of a transistor with a gain factor of 500. Theoretically, a transistor with a current gain (Hfe) of 500 can increase that current to 3.75mA. Using that signal, the subsequent stages only need to have an overall gain of 32,000. Between the various amplifier stages in a given unit, that is easily accomplished at low current/power levels.
Back to that "practical limit" of voltage and current in a transistor amplifier, as currents increase the gain factors of transistors tends to necessarily decrease due to heat/power dissipation (wattage) limits. This explains why power transistors commonly have Hfe factors well under 100, sometimes 25-40. A larger output transistor driving an 8Ω load with Hfe of 50 would theoretically need a 30mA signal applied to its base to achieve that 12V output level. That will determine what the preceding (driver) stages need to accomplish.
That is all theoretical, and in practical applications there are limits, losses, and a desire to have a safety factor (overhead) for durability. What it indicates, however, is that gain required in a given stage of the amplifier to achieve the desired result. If a particular stage only needs to have a current gain of 150, installing a device with a gain of 250 may not produce any advantages. Conversely, if a stage needs to have a gain of 250 and the device installed is rated to 150, the resultant output signal of that stage may not drive the subsequent stage to an adequate level. That will often result in distortion since the clipping of the preceding stage would only be amplified but the subsequent stage.
In short, a little math will need to be applied to engineer an appropriate replacement device. Which board/stage is invovel in your SX-939?