What is the difference of ControlValueAccessor and banana in a box syntax in implementing two way binding?

I just found out that there are several ways to implement two way binding in a custom component. What I can't understand is the difference between them. When shoud I prefer using a component which uses banana in a box syntax (with an @input() and @Output() for the model), to implements two way binding like this component

@Component({
  selector: 'app-first-component',
  template: `
    <p>input model value: {{ inputModel }}</p>
    <button (click)="clickHandler()">Clear</button>
  `
})
export class FirstComponentComponent {
  @Input() inputModel: string;
  @Output() inputModelChange = new EventEmitter<string> ();

  clickHandler(): void {
    this.inputModel = '';
    this.inputModelChange.emit(this.inputModel);
  }
}

and one which implements ControlValuAccessor like this

@Component({
  selector: 'app-second-component',
  template: `
    <p>input model value: {{ inputModel }}</p>
    <button (click)="clickHandler()">Clear</button>
  `,
  providers: [{
    provide: NG_VALUE_ACCESSOR,
    useExisting: forwardRef(() => SecondComponentComponent),
    multi: true
  }]
})
export class SecondComponentComponent implements ControlValueAccessor {
  private inputModel: string;
  private onChanged: (value: string) => void = () => {};

  clickHandler(): void {
    this.inputModel = '';
    this.onChanged(this.inputModel);
  }

  registerOnChange(fn: any): void {
    this.onChanged = fn;
  }

  writeValue(value: string) {
    this.inputModel = value;
    this.onChanged(this.inputModel);
  }

  registerOnTouched(): void {/* ignored */}
}

I they're used in a parent component like this

<app-first-component [(inputModel)]="value"> </app-first-component>

<app-second-component [(ngModel)]="value"> </app-second-component>

As you can see they are used in the same way and also do the same job. If so, why is there ControlValueAccessor? Is there anything I can do with the second component which is not feasible with the first one?