An analogy may help to visualize this:
Think of the transistor as a valve or faucet. The base is the knob, the water tends to flow from the positive side (storage tank) to the ground (drain), if you follow the normal "current flow" directions.
The LED is like a little transparent glass section in the pipe, with a small ball loosely held in that section.
When the faucet is opened, water will be allowed to flow, and the little ball will jump around due to the water's flow.
This will happen whether the LED is above or below the faucet section.
Now for the case of electron flow, as opposed to conventional current flow direction.
Consider the same pipe and faucet, but with the ground being a source for some gas, say natural gas at high pressure underground.
The Vcc is the open air, normal barometric pressure.
Again, as the faucet is opened up, the gas will flow up the pipe, the little ball will bobble around. Again, the glass pipe section (LED) could be before or after the faucet, it won't matter.
I hope this analogy helped.
If you wish to avoid holy wars you'll need to avoid making simplistic and incomplete statements :-).
Bipolar transistors are current driven.
MOSFETs are voltage driven.
In both cases the spread of parameters during manufacturing is such that a circuit will almost always rely on feedback to produce a given voltage or current gain.
MOSFETs tend to be slightly more costly at the very bottom end for "jelly bean" applications. But, for switching more than a few ~100mA, MOSFETs are usually as cheap or cheaper than functionally equivalent transistors, are easier to drive from a uC (microcontroller) as a digital switch than bipolar transistors and tend to have very significantly superior on characteristics.
An "on" bipolar transistor exhibits a saturation voltage. This can be several tenths of a volt and to get it much under 0.1V usually requires a high base to collector current ratio that is undesirably high. At 1 A a 0.1 \$V_{sat}\$ (saturation voltage) dissipates 0.1 W and is the equivalent of a R = V/I = 0.1/1 = 100 \$m\Omega\$ transistor. But at 10A the figures are 1 Watt dissipation and 10 \$m\Omega\$. The 0.1V is very difficult to achieve at higher current levels.
The \$R_{DSon}\$ (Drain-Source on resistance) of MOSFETs is typically under 0.1 \$\Omega\$ and you can get devices with 10 \$m\Omega\$ or even sub 1 \$m\Omega\$.
As switching speeds rise MOSFETs need a gate driver to charge and discharge the gate capacitance. These can be relatively cheap.
More soon ....
Best Answer
There is a very simple way to measure it. You'll need a voltage supply rail that is high enough to reach the voltages you want to test, of course. (\$V_\text{SUPPLY}\gt V_\text{CEO}\$.) If this is a lab supply that allows you to set a current limit, use that feature. If you don't have a current limiting feature to access, then you will need to fabricate something (not hard, but again if you are using BJTs for this you need to be sure their \$V_\text{CEO}\$ is large enough.)
Just set the desired current and feed the current source to the collector of the BJT. Leave the base open, of course. Hook the emitter to the other side of the power supply. Attach a voltmeter across the emitter and collector and measure the voltage there.
The current source (or sink, depending) should be set to a value you feel comfortable with considering the BJT. Make sure that you test this current source/sink with a few different resistors to be sure that it is doing what you expect and yielding a value you want -- before applying it to your transistor.
That's about it. Don't test too long. Just long enough to get your measurement. See Vishay's Measurement Techniques for an example (Figure 3.)