Generally, using events will make your code easier to maintain.
The login check you describe seems to be instant, so approach number 1 would be ok for such a simple case.
Often the login check (or whatever process) may not be instant, for example if the CheckLogin class sent a server request and waited for the response. In this case using events is better. The Main class can listen for a LOGIN_SUCCESS or LOGIN_FAIL event and handle it when the event occurs. All the login logic stays within CheckLogin.
Also, using events will allow multiple interested classes to react, without them knowing any of the inside login process.