It's a good question, Blammo585. The part I think that you're missing is how the circuits actually behave, but maybe I can help explain it to you.
When you stop and think about the first setup, you have a 2-channel amp that can produce 100 watts x 2 at 2 ohms. That means that the total output is 100 watts x 2 = 200 watts total.
In the second setup, you have 200 watts being delivered into two subs... so each sub only gets 100 watts each. Here's how the math breaks down:
Using Ohms Law and looking at the first way of doing it:
Power = Voltage * Amperes
Voltage = Amperes * Ohms
Using substitution: Power = (Amperes * Ohms) * Amperes
Power = Amperes ^2 * Ohms
(Amperes ^2 is just Amperes Squared, or Amperes * Amperes.)
So if you have 100 watts into 2 ohms:
100 watts = Amperes ^2 * 2 Ohms
100/2 = Amperes ^2
50 = Amperes ^2
Square root of 50 = Amperes
7.07 = Amperes
So we plug that back into the equation to find the voltage:
Voltage = Amperes * Ohms
Voltage = 7.07 * 2
Voltage = 14.14
Check our math:
Watts = Voltage * Amperes
Watts = 14.14 * 7.07
Watts = 99.98 which is close enough. (Rounding errors.)
So when we look at the other way of doing it, we're bridging the two channels into a single channel. We're connecting the subs in series, so it's 2 Ohms + 2 Ohms for a 4 Ohm total load.
If the amp puts out 200 watts at 4 Ohms:
Watts = Amperes ^2 * Ohms
200 Watts = Amperes ^2 * 4 Ohms
200/4 = Amperes ^2
50 = Amperes ^2
Square root of 50 = Amperes
7.07 = Amperes
Notice that in both applications, the amplifier is putting out the same amount of Amperes. So what must be changing is the amplifier's Voltage. Let's check that one:
Voltage = Amperes * Ohms
Voltage = 7.07 * 4
Voltage = 28.28 which is twice the amount of it operating in single channel mode.
Checking our math:
Power = Voltage * Amperes
Power = 28.28 * 7.07
Power = 199.93 which is close enough. (Rounding errors.)
So if we wanted to, we could look at how the second setup is working... we know what the voltage is, we know what the current (Ampere) is through the wire, so we can calculate how much power is being used per sub.
On a series circuit, the current is the same. Each sub will 'see' 7.07 Amperes. For a fixed resistance of say 4 Ohms, and using Ohms Law:
Voltage = Amperes * Ohms
Voltage = 7.07 * 4
Voltage = 28.2...so that checks out. But if we look at each of those 2 Ohm subs separately:
Voltage = 7.07 * 2
Voltage = 14.14
Power = 14.14 * 7.07
Power = 99.96 which is close to 100 watts.
So each sub will be getting 100 watts no matter which way you decide to wire it.
Hope this helps.
Mark