Should receipts be recorded using the date the money was received or the date the money was deposited in the bank accounts?

That date money was recieved...

receipts should be recorded on the date the money is received.  It affects your a/r aging if you wait.  Moreover not every company deposits money every day.  You may send out customer statements where there is no record of the collection and therefore upset or disrupt the trust between your company and customer relationship.

should be recorded the date the money was received

it depends business attitude of the management . For some one it suits the receipt recording at the receiving date of the money of the instrument of payment which is in the beneficial for those  employees having responsibilities of debt collection well in time and conservative management will record the receipt upon crediting the money in the accounts.   

Cash receipts should be recorded with the date the money was received. For example, a church collects money during each of its services on Sunday, June 4.On Monday, June 5, the money is counted and is deposited into the church's bank account. The transaction to record the cash and the revenues (remember double entry) should be dated Sunday, June 4, since that is the day of the transaction—the day the church received the money.The day the money is deposited into the bank account is not the proper date of the transaction. The accounting records should report that the money was received on Sunday, June 4.

RECEIPTS IN CASH / CHQ SHOULD ALWAYS BE RECORDED THE DAY IT HAS BEEN RECEIVED. IT  HAS MULTIPLE ADVANTAGES.

1. IN CASE OF CASH (IF THE CASH IS STOLEN / LOST)  YOU ALWAYS HAVE A PROOF OF THE CASH ENTRY IN THE BOOKS ( INSURANCE CLAIM WILL BE JUSTIFIED).

2. CHEQ RECEIVED SHOULD ALSO BE ACCOUNTED ON THE DAY IT HAS BEEN RECEIVED SINCE THE INSTRUMENT HAS BEEN RECEIVED.

3. COLLECTION PERIOD IS COLLECTED CORRECTLY

4.  GAP BETWEEN CASH RECEIPT & DEPOSIT & (LIKEWISE CHQ RECEIPT & DEPOSIT) CAN BE ANALYSED TO FIND A SNAG IN THE SYSTEM OF THE COMPANY OR OF THE BANK.

The date the money was received

Recording date should be the date on which the money is received.

The receipts should issue on the date money received. Money deposited in to the bank is treated as Contra Entry, there is not party, only bank and cash accounts will be there.