To get accurate comparisons of your alternators, you will need to pick a single "light bulb" for your tests. Leave the battery, charger et al out of the loop. Measure the DC resistance of your light buld and compare that figure to the "calculated" resistance:
Rc = En^2/Pw
Rc = Calculated Resistance
En = Bulb's Nominal Voltage (eg 12V)
Pw = Bulb's Nominal Power Rating (eg 100W)
So, if you have a 12V bulb rated at 100W, the calculated resistance should be:
Rc = (12^2)/100 => 1.44 ohms
Compare the measured bulb resistance with the calculated resistance, if they are close (and they should be) you can continue, if not, repeat the process with a different bulb, or check your meter & calculations.
Once you are satisfied with a bulb, connect the bulb to the output of your rectifier. Connect your scope's ground to the ground side of your rectifier and connect your scope's probe to the positive side of your rectifier. Set your scope's voltage range to ~20V/Div; set your scope's time base to ~20mS/Div and start turning your alternator. Adjust your scope's voltage range to get as close to full screen scale as possible. Adjust the time base up or down to get a good shot of each "pulse".
DO NOT connect a capacitor or ANYTHING ELSE to your rectifier! Just the bulb & the Scope.
Measure the length and magnitude of each pulse, and the length of time between pulses. Note the Peak voltage as well as the "Average Voltage". If your scope is a DSO with a "math package" it should do this for you. If it is an analogue scope you will have to do the math. In either case, your current will be your average voltage divided by your resistance, and your output power will be your average voltage * your average current (or Vav^2/Rc).
Next, Connect a capacitor across the output of your rectifier. I would use a 100V 10uF or larger polarized capacitor. Repeat the above test. In this case the capacitor will "filter" your output somewhat and give you a better idea of what your average alternator output is.
PLEASE take some video of your scope for both of the above tests, and report the Rc of your test bulb.