Using Qt signals and slots vs calling a method directly

Signal/slot advantages:

• multiple slots can be connected to single signal, and you don't bother with allocating and freeing memory for this
• you can handle multithreading with this

Signal/slot drawbacks:

• a little slower than direct call
• significantly slower if the slot is virtual
• QObject is rather heavy thing, so you usually try to avoid constructing billions of them

More details are available here

Both approaches use signal-slot connections. In the first case, the connect call is made by QMetaObject::connectSlotsByName() called from setupUi. In the second case, you explicitly call connect yourself.

Also, the first approach is unnecessary in Qt5 when using C++11. You can modify the value in a lambda:

QObject::connect(ui->slider, &QAbstractSlider::valueChanged,
                 [this](int val){ ui->widget->setValue(val*2); });

To protect from deletion of ui->widget, you should use a QPointer:

class MyWindow : public QMainWindow {
  QPointer<QAbstractSlider> m_widget;
  ...
public:
  MyWindow(QWidget * parent = 0) : QMainWindow(parent) {
    ...
    setupUi(this);
    m_widget = ui->widget;
    QObject::connect(ui->slider, &QAbstractSlider::valueChanged, 
                    [this](int val)
    {
      if (!m_widget.isNull()) m_widget->setValue(val*2); 
    });

The overhead of signal-slot connections is quantified in this answer.

The main difference, in your example, of using a signal instead of a direct call, is to allow more than one listener.

If you directly call your widget setValue(), then only that one widget will receive the C++ signal.

If you use a Qt signal, now any other object can connect to receive the event whenever it occurs.

If you do not foresee any other object to ever want to receive the value by signal, I would not bother with such. A direct call is definitively a lot faster (between 3 and 6 CPU instructions instead of dealing with strings to find receivers!), but as Paranaix mentioned, in a GUI it may not be much of an issue (although in this case it could become a problem on older computers if you send all those signals while moving the sliderbar.)