This question boils to down which selective transparency options both coins offer. I'll start with Monero. In Monero there are three tools for selective transparency, namely the viewkey (called the tracking key in the CryptoNote whitepaper (a,B)), key images (I = xHp(P)), and the private tx key (r). Note that the letters between parentheses correspond to the letters presented in the CryptoNote whitepaper.

The viewkey allows you to see all incoming transactions for a certain account, but not outgoing transactions. More background information as to why can be found here. The key images allow you to see all outgoing transaction for a certain account. Thus, with a combination of the viewkey and the key images, you will be able to infer a balance of a certain account. The private tx key can be used as prove of payment on a case by case basis. That is, in case of a dispute, you can prove that you paid the receiver by publishing the private tx key (which you can obtain from the wallet), the transaction ID, and the receiver's address. An auditor can subsequently verify that you paid the receiver.

Basically 1 & 2 are important for auditing certain accounts (e.g. businesses and charities), whereas 3 is important in case of disputes.

There are, however, also a few things to note:

You cannot fake a balance by giving the view key to an auditor but omitting some transactions and key images. For more information, see here. Instructions on how to prove a balance of a certain account can be found here. The viewkey and key images won't show an auditor which address the account received the funds from or paid the funds to, respectively. For this bulletpoint I will quote Luigi: Oh, and a quibble. Revealing r (the private tx key) doesn't prove that you paid someone, only that that someone has received money. In practice, in an actual dispute, you'd be referencing a particular destination and TXID to a 3rd party, which would come much closer to proving to said 3rd party that you paid the recipient in question.