In your example it would depend on the controller, the math is volts x amps = watts
So 36 x 13.89 = 500 which means your controller will deliver roughly 14 amps.
And 36 x 19.44 = 700 which means your controller will deliver roughly 20 amps.
There should really be no difference in range between the two; the 700 watt setup would just be a little quicker.
Your range is governed more by the battery pack chemistry and amp-hour rating.
36 volts worth of 10 amp-hour lead acid batteries means that theoretically you could draw 10 amps for one hour on the pack, but seeing as how the rule of thumb is to never run the lead acid pack below 50% capacity* you would really only get 10 amps for ~ 30 mins.
So if you want to run your 700 watt setup with 10 amp-hour batteries and your controller is drawing roughly 20 amps and you don't want to run the pack below 50% capacity, you are looking at about 15 minutes continuous runtime, and I'm guessing that your motor/controller combo gets your bike a top speed of 20 mph max, so your range on a 10 amp-hour lead acid pack is realistically ~ 5 miles.
Go with lithium and you may get 10 miles or more.
* running a lead acid pack below 50% capacity will affect the number of recycles or how many time it can be recharged to capacity. If you stick with the 50% rule you may get 300 or more recycles out of your pack, but run it down to 10% and you will get maybe 50 recycles or maybe less.
I am by no means a scientist either, and the above information is based solely on my own personal experience.