MarkT:
The problem with current gain is that its "poorly characterised" - which is gobbledygook for "varies a lot between devices".
That's a good point! It might OK if you are dimming one LED for a hobby project, or if you are just experimenting. But if you are building a product on an assembly line, or if there are several transistor/LED dimmers in your project, every LED would have different brightness with the same "settings".
Typically, you'll design the circuit so that resistor values control everything. For example, if you study op-amp based amplifiers, you will see that the large amounts of negative feedback are used, and the resistor values determine gain. (Or you do it digitally, such as PWM dimming. 
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