From what I understand a battery will perform better, last longer with a slower discharge rate. So if a battery provides 100 amp hours and is discharged at a high rate you may only get 95 actual amp hours. If the discharge is a really slow rate you may get 105 amp hours.

So if you connect two batteries in parallel they will discharge at a slower rate than each would individually. If you seperate them the discharge rate will not decrease.

The answer should be to draw from both at the same time to decrease the individual discharge rate from each. Doing this will give you some benifit by reducing the discharge rate from each battery.

If you switch them from one to the other you really no longer have the parrallel concetion just have two batteries on a switch.