I think the additional commentary is helpful and interesting to Dennis, but keep in mind that his original question was wondering if switching his tube amp to the 4 ohm setting would give him "more power."
It won't.
Of course, unlike the car analogy, there is no clutch to burn out by trying 8 ohm speakers on the 4 ohm tap.
Dennis, I'm working on a slightly longer reply that may help you better understand how tube amps deliver power to a speaker. However, generally speaking, if you have a 50 watt tube amp, that is the most it is going to deliver before clipping. Doesn't matter if you have an 8 ohm speaker or a 4 ohm one. Nor does it matter if you use the 8 ohm tap or the 4 ohm one. If you are on a quest for "more power" then your solution is to buy a more powerful amp.
This is different from a solid state amp that will often increase in power as the speaker impedance drops (assuming the amp design is capable of delivering the extra current. Many amps aren't.) Of course, even in this case, the power issue is driven by the impedance of the speaker and not a setting or switch on the amp. (Think of a wall outlet. A 15 amp wall socket can deliver about 1800 watts of power. If you plug in a clock radio, it draws maybe 10 watts no matter what the wall outlet is capable of providing.)
Here's a bit of additional information that I've added to this post in an edit.
Let's say your output tube is at 400 volts and needs to see an impedance of 4400 ohms. Obviously your speaker isn't going to be of any help handling things straight off the tube - the voltage is too high for the speaker and the speaker's impedance is too low for the tube. The transformer handles the conversion from a higher voltage to an appropriate lower one for the speaker but still allows the tube itself to see the correct impedance.
The transformer has two sets of windings in it. One set of windings has a lot of turns that is connected to the output tube. This gives the higher impedance needed by the tube. The other set of windings has a much lower turn count and is connected to the speaker. The ratio of the high turn count to the lower turn count reduces the voltage at the output. The tube gets its high impedance and the speaker gets a lower voltage.
The selection between an 8 ohm and a 4 ohm speaker connection is accomplished tapping into the speaker side of the 8 ohm transformer windings before they are finished. This gives a still lower voltage at 4 ohms than at 8 ohms, so the total power output stays the same. (Assumes an 8 ohm speaker connect to the 8 ohm tap and a 4 ohm speaker connected to the 4 ohm tap on a tube amp.)
However, what some have talked about is the fewer number of turns on the 4 ohm winding has a lower DC resistance. That means it absorbs any back-EMF generated by the bass speaker driver better than the 8 ohm tap which has a higher resistance. Whether this extra dampening factor is of any use in a particular set-up depends on the speaker involved and a host of other factors, not the least of which is the personal preference of the listener. Just give it a whirl and if you like the 4 ohm tap better, great! Just keep in mind that using an 8 ohm speaker on a 4 ohm tube amp tap will effectively result in a bit less power, not more. So there is a trade off and you have to choose which is more important to you.
