For both cases money stays in bank card account. It is only a different physical tool we are using for payment execution and as everything has its advantages and disadvantages. Let's look at them. 

Mobile wallets allow payment without the need for a physical card. You just place your mobile device with the wallet next to an NFC reader and payment done. Even more, mobile wallets come with security advantages compared to a physical card, if to compare purchase in a store.  

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First, multi-factor authentication is happening such as fingerprinting or face scanning to allow a payment. When using physical cards merchants rarely require confirmation of the identity of the cardholder.  

Next thing important to mention, that the card in the mobile wallet can't fall from your mobile pocket or be stollen. The thief must be able to unlock the phone and authenticate in the mobile wallet. And even more, physical card data could be pictured by fraudsters while using it. In mobile wallet card numbers are replaced with a random generated number, called a token and never shared directly with merchant. 

 

The higher level of security can also mean lower interchange and card scheme fees for some mobile wallets. 

As well as there are some disadvantages while using a mobile wallet. Some merchants do not accept contactless payments as they do not have the necessary technology in place, so you need a physical card. Also, your phone could discharge. Some ATM do not support contactless, so you will not be able to withdraw money.