Watershed would be my biggest concern...Your neighbor's pond looks to be in the 1/4 acre size AND I do not see much erosion from it's discharge, meaning that is does not outflow too much water. With that said, I would think that your neighbors pond has a proper (or, possibly, a less than proper) watershed (does their pond stay at full pool or does it drop low in the dry times?).

Where is your pond going to get its water if you do not use the discharge from the other?

AND, Will there be enough watershed if you do use the discharge to fill your pond that appears to be closer to the 1/2 acre size?

You will have created enough pond to require watershed for approximately a 3/4 acre pond in total and if his is just right, your will struggle to keep water as a decent level.

Welcome from West-Central MO!

Fish on!,
Noel