Let's assume basis is zero, so 1065 has gain of 300. So half of the gain 150 is passed through to each partner as 75 each and half of the gain 150 remains on the installment plan, again half eventually passes through at 1/10th each year. 

Why does the non selling partner get the whole note and the buying partner get all the cash? That's not right.

The reality should be cash from buyer to partnership 150,  note 150 to partnership. Buyer gets 75 cash and a note for 75(which is cancelled, meaning his gain 150 is all in this year), other partner gets 75 cash and a note for 75. Buyer pays ex partner 75 over 10 years.