Ahab. Your dogs may behave great while under voice command, but what happens when you go in the house? Animals do not know boundries, they go where they wish when unattended. I have near fifty years experience working and training dogs, for hunting, for police work, and for the military. Dogs generally respoind well to a handlers commaand while under their control, but once the handller is gone, the dog acts on instinct. If a rabbit, or another dog comes by they WILL chase it. They may come back, but that depends on the homing instintc.
The electrict fence is a fairly good method to control dogs, but is not truly effective 100% of the time. The only way you can ensure 100% control is to have a proplerly constructed and maintained fence. The fence should have a barrier to prevent digging under, be constructed to prevent going over, and be sturdy enough to hold the breed intended. I always liked to overbuild for the peace of mind.
Bottomline, electric fences are effective to a degree, but are not 100%. If I had beagles, I would not trust it to hold them if a rabbit, cat, or another dog came by.