Generally speaking what visual performance improves might be gained by moving to Qt5.0+? I understand this is quite the loaded question on several fronts.
I assume that you have widgets-based kiosk application where almost everything is done by Q(Graphics)WebView. In this case, moving to Qt 5.x may be very important for you because it allows you to use newer WebKit.If your application allows browsing untrusted content, e.g. arbitrary web sites, using older WebKit may be dangerous because of unfixed security vulnerabilities In addition to security matters, QtWebKit 5.212 is much more compatible with moder Web content than older versions Even if you have control over the content that you disaply in your "browser", using newer WebKit allows you to use modern Web technologies like ES6, new HTML and CSS features etc.
Now about "hardware graphics acceleration". It's possible with both Qt 4 and Qt 5. In Qt 4, hardware accelerated graphics is possible with DirectFB or platform-specific QWS plugins. You also can use OpenGL, in this case you need to use QGraphicsWebView with QGLWidget viewport (in Qt 5 there is newer QOpenGLWidget).