There will be a performance issue when you execute
<button onClick={() => deleteAccount()}>Delete My Account</button>
as every time render() is called, it will create a new anonymous method which will delete the account. Also, with the above approach, if you want to use event object explicitly given by the onClick method, you need to modify your code as
<button onClick={(event) => deleteAccount(event)}>Delete My Account</button>
Whereas, when you use
<button onClick={deleteAccount}>Delete My Account</button>
assuming you are using either the bind method in constructor or using the arrow operator, the anonymous function is not created every time render method is called, but created only once and used. This improves performance. Also, the other aspect, all the parameters passed from the onClick method will be passed to the method directly.
onClick={deleteAccount},deleteAccountwill receive theeventobject as a parameter. If the function uses the parameter thinking it's the account object or something like that, it could create a funky bug to track down.